Tentatively, I'm going to say no. I have worked on Roman burial practices and death and have never encountered anything about it.

Roman emperors and senators usually practiced cremation which I believe makes it very hard to extract DNA. It also makes their remains highly susceptible to getting lost. That said, Roman burial practice shifted around the 2nd cent CE and inhumation became much more widely practiced. Still, the type of inhumation practiced in Rome is nothing like mummification and it is hard to get much information from the bodies that we do have. There is still some debate about who switched to this new practice and who didn't (it seems a lot of these sarcophagi were built for wealthy freedmen, not the senatorial class). Also, the practice of chucking a whole bunch of people into a sarcophagus/reusing sarcophagi makes it very hard to identify who the person buried in there was even in the few cases where the sarcophagus names its occupant.

Still, there were some inhumations in the earlier period such as the senatorial family the Cornelii. I don't know if they have actually found and extracted dna from any member of this family or perhaps a later emperor. It's an interesting question.