The short answer is Yes, they can. Like playing a christmas carol on the flute or trumpet, the melody for many carols will fit within the notes available to the chanter. One potential problem is that the pipes are either on or off, and not switched between the two (usually) during a song or tune. And we only have 1 key. So many carols can be forced to fit, but I would suggest without the backing of a choir, orchestra, or at least organ there will be large gaps in the tune as played on the pipes.
Another unanswered question is should the carols be played on the pipes.