First of all, there's no degree you can get that will increase your chances of being a sitcom writer. Anyone can do it if they have the talent . . . which is both good and bad. It's nice that sitcom writing tends to be based on talent, but it would also be nice if there were some training course that could guarantee your admittance into the big leagues. You don't even have to be a funny person, just a funny writer. Of course, it goes way up from there.
Chances are, yes , eventually.
It just happens to be where most of the sitcom writing work is. Furthermore, there are tons of connections to be made in Hollywood that you just can't get anywhere else. This is where blind luck plays a part. You meet someone in the grocery store checkout line, talk a little bit, suddenly find out that he's a TV producer, and he'd like to see your work. He'll give you the right name to put on the envelope to make sure that the right people give it consideration.