In short: maybe. “Roman” was a legal status, the status of a citizen, and the rules for citizenship varied depending on time and place in the Empire. During the time period that saw the burials at Casal Bertone and Castellaccio Europarco, perhaps up to 35% of the population of Rome were slaves, and many of those probably arrived at Rome from somewhere else. Slaves were definitely not Roman, because they were not citizens, even after emancipation.
The people whose DNA we will study are an unknown population: without inscriptions, without historical records, without grave goods, all that can be said is they were of the lower-class, which composed just under 99% of the population of Rome. These were average people – men, women, children… free, enslaved, freed… workers, parents, subjects of Imperial power.
The title of this website – the Roman DNA Project – is then a bit of a misnomer. We’re not going to know if we’ve found “Roman” DNA, but it’s also impossible to say what “Roman” DNA would be since that changed quite often over the duration of the Republic and Empire. What we will get is DNA from people buried at Rome, which is pretty cool in itself.
Roman DNA Project 
Good point on defining what is ‘Roman’. This is becoming an issue for me with looking at burial practices in Roman Italy, Roman Greece and Roman Britain. Figuring out who what Roman burial practices were is completely different from looking at the burial practices for a single ethnic community. I look forward to seeing how the concept of ‘Roman’ fits into your examination of DNA in a specific population from Rome. It definitely makes it more complex!