Is it possible for an F6 tornado to occur?

Yes and no. While it might be possible for winds in excess of 318 mph to occur, Fujita scale ratings are based on damage rather than winds speeds. So even if winds in the theoretical F6 range were to occur the tornado would still be rated F5 as F5 winds will obliterate all man-made structures leaving no room or purpose for a higher category to be used.

So the F6 rating is purely theoretical.

On the new Enhanced Fujita scale the EF5 wind range has been left open-ended so there is no EF6 theoretical or otherwise.