Answer
Yes.
Work Step by Step
An electric current is produced by a net charge (sum of all charges, positive and negative) in motion.
The comb, before rubbing it through the fur, was electrically neutral (net charge was zero).
After rubbing it through the dog's fur, the comb's net charge changed (it is not zero any more).
There is a net charge on the comb, and it is in motion (you are moving it), so yes, an electric current is produced.
