Fast powders can have less fouling, but they don't always. Most Alliant powders are dirty, especially Bullseye and Unique. Though Power Pistol is supposed to be extremely clean. Clays is one of the fastest powders out there, and is also very clean. But so is Universal, which is somewhat similar to Unique's burning rate, at pressures below 30,000 PSI (do not use Unique for calibers that generate more than 30,000 PSI). There really are no hard and fast rules about fast powders being cleaner.
Although if you use a powder that's far too slow for your gun/cartridge combination, you'll end up with a lot of unburned powder grains all over the place.