Not according to Dracula's Guest. In which references Carmilla as another vampire contemporary to Dracula, albeit under his command yet unknown if she was made by him.

However I'll make adjustments and make him a sorcerer who was made into a vampire later. Which would simply explain the age.

Furthermore, in Dracula, the good count's appearance changes over time actually. He was considerably older at the beginning of the novel than at the end which is suggested by his feeding habits. Hence why the 3 images.