Yes it will work - that is what the GB bridge was designed for. Not all GBA flash cards are compatible with the GB bridge though. I use a Visoli GBA flash card with GB bridge on my GBC. I also use Pogobridge to make life easier with saves.
Yep, getting the original games is a far better idea and much less hassle. I recommend that you also look out for Mario Picross, Tetris DX and Pokemon Pinball.