I would not say that. The Democratic party may indeed have its roots in the Democratic-Republican party, but I wouldn't go so far to say they are the same party, the simple fact remains that a D-R candidate from yesteryear would not fit at all in the Democratic party today.
Some people would agree and point out that the co-opting occurred about the same time they took the word 'liberal'. That group has shown itself as skilled at camouflage as a chameleon.
For the most part they wouldn’t fit in. However there were some, those who set up Jacobin clubs, who would fit in today. They had their share of Robespierre supporters who would feel at home in today’s Democrat Party.