Hi kahuna, and welcome to the world of MorphOS.

Bluetooth is not specifically supported under MorphOS, though I'm typing this message using an Apple A1016 Bluetooth keyboard that I paired via Mac OSX and it works as intended with MorphOS, but there is no Bluetooth 'stack' that is part of MorphOS.

Having said that the A1016 is an old Bluetooth keyboard that Apple made in the era that the G4 & G5s were being sold by Apple, as is the A1197. However, it being Bluetooth, rather than it being a wired or a standard wireless Mighty mouse, may have functionality that MorphOS's capabilities of understanding bluetooth devices just can't handle, but as Kronos said if you can get it to recognise the function with prefs then you're in with a chance of some good luck!

I generally use a Logitech T-RB22 trackball that's wireless and that works great with any system I've tried it with, but it's not Bluetooth hardware.