Certainly Bob Cratchit is incredibly mistreated by his employer, Ebenezer Scrooge, and he does manage to retain his basic human dignity. His holidays still have meaning, he provides for his family and takes great pride in that provision, and he truly loves his wife and children and is clearly very loved by them in return. His life does not lack meaning or dignity simply because he is treated poorly at his place of work.
It isn't the way Bob's treated that can or cannot affect his dignity, it is the way he handles this treatment, and he seems to take it more as a reflection of Scrooge than of himself. Despite Scrooge's awful loathing of Christmas, Bob wishes him a happy one anyway, and he manages to make his family's Christmas happy despite his employer's stinginess. The description, too, of his family's perception of their meal -- that the little ones are "steeped in sage and onions" up to their brows, and the great oooohs and ahhhhs that greet the presentation of Mrs. Cratchit's rather small goose and pudding -- indicates that they feel no loss of family dignity despite having to drink their Christmas punch from old dishes and a single, well-used cup.