If anyone else is wondering about this, I went ahead and did some testing of my own with the Photoscan trial and the Doll set on the Agisoft site.
First up, there doesn't seem to be any problems running NVIDIA and AMD cards. Photoscan will use an AMD card to process while an NVIDIA card is running the display, so that's good.
Second, I didn't see any benefit from Crossfire, but I did see a benefit from having multiple GPUs. Here's some numbers I got for the Dense Point Cloud generation:
No GPU, 4 CPU cores: 503s, 500s
Radeon 7870, 3 CPU cores: 343s, 351s
Radeon 7870 x 2, No Crossfire, 2 CPU cores: 302s, 302s (~16% faster)
Radeon 7870 x 2 in Crossfire, 2 CPU cores: 308s, 307s
So it looks like Crossfire might actually hurt performance a bit, but doesn't seem to help at all.
Hopefully this helps anyone else with the same questions I had.