Rockbox is also sort of close: http://www.rockbox.org/

I guess it already supports more chips and screen sizes than something aimed at TI calculators would.

But can it really be called an operating system?

I think so. There's a gameboy emulator in there:

http://www.rockbox.org/wiki/PluginRockboy

I guess it would be more applicable to the bike computer use case than a phone. But who knows.

You certainly could replace the memory chip of whatever device you want. Chances are, as long as it has a few necessary components (or code to emulate them) Linux will run pretty well.