A Christmas Carol (assuming the book by Charles Dickens) could be a play, but it must be adapted first to a shorter version where it is suitable to be used as a play. The length, things you cannot do on stage that occur in the book, and more must all be taken into consideration.
There are many different adaptation of the Christmas Carol play that have already taken place to easily state that this is definitely in the affirmative. The play itself has been remade in to at least a half a dozen different movies that play on the same theme with sometimes major changes. Therefore the play A Christmas Carol has already been shown to quite adaptable.
The story "A Christmas Carol," a novella by Charles Dickens, has had many adaptations, from Muppet versions to film, but most popularly as a play. This is easily done because it is a simple and repetitive story that is easily understood from audience to audience, all of whom are inspired by its message of Christmas cheer and overcoming selfishness.
I should think A Christmas Carol would be tricky to adapt into a play, as ghosts by their very ethereal nature would be hard to depict convincingly. I suppose smoke and lighting effects might make some attempt to make the ghostly characters appear and disappear effectively, but not nearly as well as CGI for the screen, for instance.