I don't see why you couldn't. It is just a matter of researching your supplies properly. I am sure you could build a decent grow chamber for 50-150 dollars. It all depends on how much you want to grow and how good of quality you want your crops to be.
ya its possible, but dont invest a cent till you do research. alot of research if you have no formal experience with plant life (science class, garden, ext.)
seriously before you start deafinately do your research but i have a working grow area for about $80, i did alot of thinking outside the box to accomplish that but it worked.
i painted a corner of a room flat white $6
got some elmers flat white lamonated foam board and used duct tape to fill in the other corner.$4
got a couple of 40w cfl's$40
pots$3
compost$10
timer$2
fan $4
and any nutes