Not really. And it has more to do with the nature of the New Testament than with anything else. The NT is a small corpus with limited scope written in relatively bad Greek.

Scholarly consensus is that Paul's letters were written closest to the time of Jesus' death. Even so, things like the privileges of Roman Citizenship, his description of social ills in the city of Rome, and the dangers of Mediterranean travel are all better attested to by relatively contemporary sources.

The NT has volumes to tell us about the social phenomenon of Christianity, but in terms of general Roman history there are much more thorough and specific contemporary sources.

It's important to clarify what OP means by "purely Roman history." The city of Rome itself? The Latin-speaking west? Those with Roman citizenship? Or the Roman Empire as a whole? To historians, "Roman history" without any other qualifier is an expansive term, covering everything from the early kings to the Empire and beyond. I focus on Roman Egypt, for instance, and deal with evidence mostly written in Greek (and some Egyptian), but still consider myself a Roman historian (and hope others do too!).

If we're speaking of Roman history in a wide sense, I must disagree with /u/stayhungrystayfree and argue that the NT is an incredibly valuable source for the social history of the Empire because it gives us insight into non-elite aspects of society (as /u/LegalAction suggests as well). It's important to stress that most extant ancient literature was produced by and for a relatively small network of literary elites and therefore rarely pays much attention to more marginal figures or groups, except by way of offering generic contrasts. A large body of literature, moreover, from a group that was not always "on board" with the Roman order is valuable indeed.

The works of the NT tend to be thought of as different b/c of their canonization and incorporation into what became a massive religious movement. But many of the works are not much different in approach and style from contemporary, non-Christian works. The Gospels, for instance have much in common with Greek βίοι, "lives," what we would biography (Burridge 2004), even if they are also influenced by the language of the Septuagint and Christian theology. Take a look at Philostratos' entertaining biography of Apollonios of Tyana, a figure who's often been compared to Jesus.

Burridge 2004, What Are the Gospels?: A Comparison with Graeco-Roman Biography.