Definitely possible. But if you're gonna resort to pharmaceuticals, why not just go for ones designed specifically to treat anxiety?
Like qwerty says, they're just temporary, have side effects, and you have to take em for the rest of your life.
I prefer to deal with it on my own and try to overcome that (although that hasn't exactly worked so well lol) but I read about how others take anti-depressants and stuff, and even though it balances them out, they say it's kind of like being in a dream or like a zombie forever when they're on it.