No, unless he appeared in a secret uncredited cameo, Liam Hemsworth has not appeared in Under the Dome.
Perhaps you are getting confused with Under the Dome's lead actor, Mike Vogel? They look a little similar when fully 'bearded'!
Here's a picture of Mike Vogel, can you see what I mean about the beard?
As for Liam, it looks like working on the next two Hunger Games films is going to keep him busy for a while yet. Here's a video I enjoyed of two THG fans look at the trailer for the next sequel:
