Yes, according to Harper's Dictionary of Classical Literature and Antiquities. Before 300 B.C., all Romans (who could grow them) had beards; it was after a barber came up from Sicily that they started to regularly shave. Short, ornamental beards became somewhat common, but unkempt beards became an indicator of "slovenliness and squalor." Exceptions were made, though, for men in mourning. Notably, Augustus grew a beard when mourning the death of Julius Caesar.