Yep, you can do fair isle in the round! I've done several hats with fair isle on them.
And yes, fair isle in the round will have the same issues as doing a stripe would. Because knitting in the round is a spiral it will be off a bit off, but it seems to show less than it does on a stripe. On the right side you can see the "off" bits. In a very detailed pattern you might not notice it at all.