It depends. WHICH Batman, the one in the current film franchise, the one from the current monthlies, the one from the Justice League, etc etc?
I am going to make an assumption here, in order to best answer your question. We'll put aside the issue of Batman trained by ninjas in the films, or the question of whether in the comics Batman operates with sort-of-superpowers when interacting in stories alongside Superman and other such characters. By "become Batman" you mean the basic concept of Batman that we all could agree upon -- a master of martial arts, of forensic and detective skills, of gymnastics, of science and chemistry, of history and geography, of the workings of organized crime, of criminal psychology and physiology, and a man with a suit offering protection against bullets and knives and electrocution but which allows him to move as fast as an Olympian runner and acrobat.
The simple answer is, no. Unless you really boil Batman down to a very diluted level as just a really strong, fast, good fighter who can jump far and with good street smarts plus an education in crime and psychology, and who wears a lot of armor and a mask.
The genius of Batman is that it pretends to be realistic, it lets us convince ourselves that with enough money and training, we could become Batman, too. But it's still fantasy, it's just a fantasy that is more compelling and convincing and thus more fun.
If you joined the military and became something like a Delta Force commando of the highest quality, while studying nights to get a double-major in criminal justice and psychology, with a minor in chemistry, you might also have time to take weekend courses in detective work and get a P.I. license. Then, after probably 10 years to reach all of those levels combined, you might be 28 (if you started right out of high school) and would then need to maintain your physical level while getting a job as a police officer in order to learn real crime solving and detective work on the streets and at crime scenes, to get the experience it would really take to be a master. Let's say you are so good it only takes you perhaps three years to become a top detective and expert in these regards -- now you are 31, and just finished the most basic level of preparation you need to be an expert in just some of the most obvious fields required to match Batman.
Now you have to quit the force, and develop a good cover story for yourself so nobody suspects that Batman might be the guy who is an expert in all of those fields Batman is a master at. You have to have made sure you lived your life never revealing your true feelings about crime and vigilantism etc, and in fact covering it up unless you want to be arrested as a suspect the first time Batman has been around town. You need to spend some time doing dry runs around town to find your way around rooftops and fire escapes, practice running around at night in the shadows and not being seen, and presumably start practicing using your ropes and grappling hooks and other equipment you need for nightly patrols. Do some dry runs, make final preparations in case of emergencies, etc.
And you need to have been investing money and amassing a fortune the entire time, because the technology you'll need to even get close to a real-world version of Batman will cost millions of dollars. So you've done that, and now you start spending the money to get an armored suit full of electronics to communicate with assistants and have night vision and so on. You need a base of operations, so you buy one of those old used missile silos the military sells (yeah, they really do that, and it's pretty cool inside them) and turn it into a secret headquarters for the computers and monitoring equipment and car and bike and other equipment you need for your vigilante life.
Conservatively, you should probably be about 32 at this point. And you are only about to go out on your first night as Batman. Okay, it's taken longer than expected and been pretty hard, and honestly you are not quite as much a master of all fields as Batman, but at least you got the basics and are pretty well trained and smart and equipped. So off you go, looking to stop crime...
...and you're looking. And looking. Oh, wait, you hear police sirens or you get a transmission from picking up the police radio calls, there's a domestic disturbance in progress... well, that's not really what Batman does, so you let that one go to the cops. Then you get another call about a robbery, ah ha! Finally Batman is going into action! You run across those rooftops, swing across to another roof -- whoa crap, that was a lot more dangerous than it looks in the comics! But you're booking it, running flat out and probably hitting, what, a good 10 miles per hour? Maybe less actually because of having to dodge things and stop at the edge of the roof to swing down again.
Anyway, there you are, rooftop to rooftop, and it occurs to you that the cop cars are so far gone now that you barely hear the sirens. So you think "Hmm, no wonder the real Batman has a car, this rooftop thing looks cool but I'll never make it in time to stop a crime that isn't happening within a block or two."
And you don't -- make it in time, that is. The first few nights, you keep showing up and the robberies or shootings or whatever are already over, and you realize that this makes sense because most reports about crimes are only after it happens, not while it's taking place. And you also remember that as a cop, you almost never just walked up or drove up accidentally right where a crime happened to taking place. In fact, you were just one of several thousand cops in your city, and most of you never just stumbled right across a significant crime in progress.
By your second week, you are getting unhappy that 90% of the crimes you've even seen up-close are just pathetic junkies buying crack from another pathetic junkie selling drugs to support his/her own habit. And nothing makes you feel LESS like Batman than scaring sad homeless crackheads. You tried to chase down a kid who you saw punch a lady and take her purse, but you can't really pursue that kind of thing by running on rooftops, you gotta do it the hard way by chasing him on foot down the sidewalk... in your full Batman costume, where everybody can see you. People are taking photos on cell-phones, and yep there's a cop car at the intersection and he saw you, and now he has his lights on and it's YOU he's after. Great, you have to let the kid go so you can run down an alley and climb up a fire escape to the roof to get away.
At last, week three, you get lucky -- an armed robbery, right there across the street! You leap down onto the hood of their car, cape over the windshield just like in The Dark Knight Returns. And a teenage kid in the passenger seat fires a shotgun though the windshield in panic, blasting your torso.
You are wearing armor, though, haha! So it merely shreds your costume and knocks you off the car onto the street, but man that hurts! And it takes your breath away just long enough for the car to speed off. You get up, angry and just in time to see everyone taking your photo again and staring at your shredded outfit. Then the police come around the corner, and you run off again but this time you are injured because although the armor stopped the slug it still bruised you and broke a rib. You are fast, but not fast enough this time. The police draw their guns and order you to stop. You turn and grab for the smoke pellet on your belt to help hide your getaway, but unfortunately for you the cops see you reaching for something and open fire... and you suit's armor is already a mess from the shotgun blast earlier. Uh oh.
When you wake up in the ICU, your mask and costume are gone, you're in a lot of pain, but the doctors successfully removed the bullets and re-inflated your lung. The downside is the set of handcuffs trapping you in the bed. As a master detective, you can of course easily pick the lock on the cuffs to escape, but on the other hand the staph infection you caught after surgery is pretty bad and you feel like s**t. So you wait until night to sneak out -- except you fall asleep on your pain meds, and wake up the next morning to the police coming to pick you up and take you to the infirmary at the state prison. Where you will spend a month recuperating until they can transfer you to the county jail for your first court appearance. During which your only comment to the judge is, "I guess it's not really possible to become Batman."