Could Sydney Carton of "A Tale of Two Cities" be described as a dynamic character or a bildungsroman?
yes A bildungsroman in a novel shows growth of a person and spiritual nature. Sydney Carton seems to met the criteria.
Sydney Carton is a weak self centered person in the beginning of the novel. At the end of the novel he has grown spiritually to the extent that he is willing to give his life out of love for another person. Sydney states that in giving his life he is doing something better than he has done before, that in dying he is going to live.
Sydney from being a sad selfish person become a Christ like figure. Like Christ he willingly gives up his life to save the life of another person.