I don't know, but adding a new rom shouldn't be an issue. Meaning, you could use a normal FF3US rom file and upload that, instead of using the copy provided via the SNES Classic.
BNW doesn't have platform specific releases, but aims to be compatible with the original hardware (and as such, should work well with most emulators/variations to play SNES games). This doesn't mean that it works on SNES Classic, just that it is very likely to work.
Why not simply try it out? You could report your findings here, probably interesting information for more people around these parts. :]
Answered to the best of my knowledge. Knowing full well that I'm no expert in the area, I welcome being corrected.