I just did a frame swap, taking parts from a ***-brand bike and putting them onto a bikeshop frame (a Rockhopper). Here are some things I learned along the way:

1) Cheap parts tend to be on the heavy side. But if you are only moving a few over, then that may not matter. But you will run into things that you don't normally see, such as steel stems(!).

2) Many low-end parts work just fine. In my case, the chain, the shifters, the brake levers, and even Shimano's Tourney rear-derailer seemed to all work ok.

3) You may find some parts that aren't really appropriate to a mountain-bike. For example, I ran into 48/38/28 chainrings. Those are fine on a hybrid, but not what you want on singletrack.

4) Some parts won't be compatible with other frames. Seat-tube differences may mean that the seatpost and front derailer do not transfer over. And I've seen some low-end rear deraillers that come without hangers, leaving no obvious way to mount them to frames that do come with hangers.

5) Some low-end parts do not work so well. I've not had much joy with low-end disc brakes, for example. Low-end wheels don't fill me with confidence either.

Bottom-line, you can transfer parts from a cheap bike to a good one, but not everything will go over easily or well. I really wouldn't recommend going down that path. What you might think about though, is buying a low-end bike from Target -- say a Schwinn -- and riding that back and forth to school. Make it a rigid bike. It'll cost less, and simpler is better at those lower price points.