In general, there shouldn't be a problem with mixing brands/speeds of standard DDR2 RAM, just like there shouldn't be a problem using a Purolator brand oil filter on a Ford car.
However, the two RAM types you listed are unfortunately NOT standard DDR2 RAM, as each needs to be overvolted (above the DDR2 standard 1.8V) to reach its advertised speed/timings. Worse, they each require a different overvolt:
...2x 1gb sticks on Patriot DDR2 800 PC2 6400. ... it runs at 2.2V.
The RAM I want to buy is G.SKILL brand, CAS 5, timings 5-5-5-15, 1.8-2.0V. ...
All RAM installed in a machine needs to be run at the same voltage, speed, and latency settings -- they can't be set independently for each DIMM. Thus, without more information we have NO IDEA if there is a voltage where the two RAM models you mention can both run correctly.
Hopefully, both can run properly at the DDR2 standard 1.8V -- you need to contact each manufacturer and find out (a) will the specific module work at 1.8V and (b) what speed and latency settings should be used at 1.8V. These will of course be slower settings than the advertised overvolted settings.
Based on that info, you can pick a speed and latency settings that both modules will support at 1.8V. If the manufacturer won't tell you this info, they are being dishonest in selling their RAM as "DDR2" RAM.