Okay after screwing around for awhile, the GH3 wireless guitar doesn't work with GH1 or GH2.
I can literally use the GH3 guitar to screw around in the PS3 menu, select GH2/GH1, and suddenly the GH3 guitar disconnects. There's no way to get it working.
The game loads fine and you can play with the sixaxis controller (lame), there just isn't support for the PS3 GH3 controller in GH2 or GH1. It's especially crappy since there's a PS2 version of GH3 (with its own wireless guitar), implying that there may be some easy software workaround that was just never implemented.
I read something about people buying those PS2 - USB adapters and being able to play GH2 on the PS3 using the old guitar, but I heard it didn't work completely correctly (star power and strumming were both broken).
Maybe if enough people e-mail Harmonix we can get them to release a patch or something for the PS3 that lets you play GH2 and GH1 with the GH3 guitar.