It is not impossible, although the Galaga hardware that Bosconian runs on has a triple CPU setup that might prove more tricky than Galaxians single Z80. Compiling multiple games into one shouldn't be a problem, if it's done the same way as e.g. '6-Pak' where there is a boot menu and you have to reset to get back to it.
Viewing post in Galaxian for Mega Drive / Genesis comments
Showing the HUD like the arcade game requires a few more vertical lines of resolution than the Genesis has. The only option would be to display the whole game rotated 90 degrees. It may be possible to do, but I think it has too limited a use case to be worth it.
The attract mode (Game Over/We are The Galaxians) should be the same as the arcade game, what is missing?