A GBA is not a computer, but some of the data is stored in similar, if not identical manners. I am not supposing that a computer could successfully enact a transfer, but a computer-like device that was adapted to the particular data-storing methods of the GBC and GBA might work.

I still think the chief problem in such a task is that the data storage between the GBC and GBA games is likely very different, even beyond simply being on different systems. There are many other factors to manage on the new games, including but not necessarily limited to ribbons, EVs, traits, etc. I believe that this might be the most difficult obstacle to overcome. The technical difficulties of electronically linking a GBC and GBA might be manageable, but I think that this problem would prove to be quite a difficult one to anyone who undertook it.