would I be able to program bits and pieces of the program on the board that I was given for my class and then transfer the program to the other board
Basically yes.
If you give all PIN numbers as variables, or in form of #define statements, then their is only one line to change for each PIN number if it needs to be changed from one board to the other.
I would have thought that your big problem is going to be the vibration sensor, these things are not that sensitive and you might have trouble detecting such a low mass impact.