I find the idea of a GameBoy Classic pretty suspect. Unlike the NES and SNES Classics, you can't have the games in HD on a big bright TV display. The system itself can't be more "mini" than it was in the first place without ruining the screen size and the button layout. In terms of game quality it would be perceived as a big step backward from the SNES and would need a lot more games included to be appealing. On top of all of that, you can still pick up and play your GameBoy or Pocket today by just sticking some double-A batteries in it -- unlike the NES and SNES which almost nobody has kept around, at least outside of a closet and next to their HDTV with some kind of converter necessary to even display it.
All that to say, if there is actually going to be one (and they didn't just trademark the name to prevent rip-offs), I think it would probably be a "GBA SP Classic" which includes GBA, GBC, and GB games. That way you have something much closer to modern tech as a base, including a bigger and backlit display, and can include the other games with backwards compatibility.
Sure, you miss out on the nostalgia factor of the original GameBoy hardware, but I don't think the tradeoffs are worth it to go that route.