You'll definitely have time, but a lot of it has to do with you and the cat you end up with.
I got a 5 month old kitten after I was in med school for one month. But it turns out he's a pretty needy little kitty. He doesn't like being left alone a lot so I mostly study at home (which is hard for some people). He likes butting into my notes when I'm studying and tends to have some early mornings where if he's up clearly I should be up.
As others have said, things to consider:
1) Can you study at home so your kitty isn't neglected?
2) Will you have someone to give him too/someone to check on him when you are away for interviews etc?
3) What are you going to do for breaks? If you are going to school far enough away that you need to fly home keep in mind only a few airlines take pets (Southwest isn't one of them) and its pricey and a lot of animals don't deal with flying very well. I'm close enough to my parents that he drive the 75 minutes home with me.
4) Will you have to move during med school? I am moving closer to the hospital for the 3rd year and I can't live in the complex that I REALLY want because they don't accept cats at all. Depending on the city you live in it can be easy or hard to find a place to live that accepts cats.
5) Cost. Can you afford it? Food isn't so bad. Neither is litter if you buy in bulk from somewhere like Walmart (probably about 20-30/month). But you will also need toys (enough that they are rotated out so your kitty doesn't get bored), and you need to keep in mind that if something goes wrong costs can go up. Vets are horrendous. I started walking my kitty outside for a few weeks and he got fleas. I spent over $400 trying to get those little buggers out of my house. If your cat destroys furniture or carpeting in your apartment its expensive to fix.
6) Time - you need to play with your kitty and be around at least SOME of the time. It takes time to clean out the litter box and its annoying when you're stressing about a big test (if you can afford it I'm a big fan of my recent purchase the Litter Robot (
www.litter-robot.com) takes me about 15 min every week to deal with litter). I also am a big proponent of the big autofeeders and waters. I have a Drinkwell Fountain for water that I refill once a week and throw in the dish washer once a month. And a little simple feeder that I feel about twice a week. For most cats having food out all the time isn't an issue if they grew up that way - because they know theres always food there they don't tend to pig out. If you find your kitty is ballooning out measure 1-2 days of food in there, when he runs out he runs out. He'll learn.
I think those are the big ones. Cats are easier than dogs but you still have to realize you have a little being that is in your control and you really need to give them the care they need.
Good luck! I love my cat and he has made med school better but sometimes he's just a big pain in the butt.