Nope, it would sound a bit impolite.:) Even if you are very close with your teacher, you should say "고맙습니다" or "감사합니다". This is how 한국어 works. \^o^/

Pretty much the only 2 kinds I hear on daily basis (in Seoul): 1. 감사합니다 - formal, polite. If you don't know, then use this by default 2. 고마워 - between friends, or to someone below/younger than you. You will here "고맙습니다", but you don't really need to use it. Just use #1, and you'll be fine. This is simpler way to learn.