Giga products will work on any processor, as long as it has enough processing power to get the polyphony you desire. Here are some actual reports:

Celeron 450 can achieve 96 voice polyphony using only Gigapiano
Pentium-III 866 will only hit about 70% of CPU power with all 160 voices (many instruments) and several plug-ins.
I have no repots from Athalon-based computers, but they should be very similar.

Latency is not affected by processor speed- only the amount of polyphony possible.

Different comptuers with different processors should have comparable latency with the same audio card and OS settings.