I don't think you could do Fair Isle in garter because the yarn has to get carried across the back. You can do it in the round or on straights, but I believe all the knits need to be on the one side and you carry the yarns on the back. When you do it on straights, you have to remember to read the pattern for the back from left to right, and you have to purl with the strands on that side, so it's easier, though not necessary, to do it in the round.
For intarsia (thats I-N-T-A-R-S-I-A) , you probably could be more flexible, but you still have a "messy" side and a smooth side, so it probably wouldn't be advisable.
I've seen purl rows and purl st incorporated in Fair Isle and intarsia patterns, but the yarn is still carried across the back and the purls are just for a more textured look.