I'm by no means a specialist on Roman religion, but know a modicum enough to say that absolutely yes, Romans, some of them believed in the gods of other cultures. "Romans", used to mean the people of the Roman Republic, and Empire, were incredibly diverse people with a huge plethora of religious beliefs and deities. What the Roman mindset did extremely well, however, was to assimilate new cultures pantheons into their own. This in turn made assimilation into the culture of the state all the easier when there is a degree of harmony. Quite often the Romans would identify a local deity with an aspect of one of their own gods - yes, you have a lovely fertility god, Mr. Barbarian, but you can clearly see that she bears a lot of similarity to our own god Ceres, so we're obviously worshiping the same deity! Examples of this can be seen in Britain, with the most obvious being the fusion of the Britano-Celtic goddess Sulis (god of the springs at Bath) an associated her directly with the Roman goddess Minerva, creating the official Roman cult of Sulis Minerva - the Britons feel their goddess is respected, the Romans are happy, everyone gets along.

There are outliers, of course. Some examples include the Druidic relgion of the British Isles, which was wiped out by the Romans. Part of this is that the Druids formed the cultural leadership of the British tribes and Rome needed them out of the pictures to remove that objection to proper, civilized Roman rule. But there was also the allegation that the Druids practiced human sacrifice, which was absolutely taboo in Roman culture. Then there was the Cult of Cybele, which was an eastern goddess and, while actually very popular, was adopted by Rome in a very specific and carefully created form that worked around the issue of, traditionally, followers castrating themselves with sherds of pottery (which undermined the masculine persona of Roman manhood). Lastly there is the elephant in the room, Christianity - which you must remember was just another cult in the early empire, with likely hundreds also emerging across the empire.

There are letters back and forth between Pliny, governing in the east, and the Emperor Trajan, were the former asks the latter what should be done with these followers of Kristos. The reply is essentially, don't bother with them, unless they really step out of line, then execute a few to maintain order. One of the notable problem Rome had with early Christians was their insistence of God being the only true god, and all others fakes. To the Roman religion this was extremely dangerous, in a very literal sense - to deny the Roman gods was to offend them, and offended gods can bring down all sorts of disasters, like floods, volcanoes, plagues, or even defeat in battle, as well as a plethora of other calamities. I remember one of my lecturers summing up Roman religious thought with the line "don't rock the boat, don't rock the boat, baby" - worship ALL the gods, everyone will be fine. Christianity upset that. By comparison, the Jewish religion actually received revered religion status in early Roman history - Jewish scholars circumnavigated the mono/poly theistic problem by considering all Roman gods were in fact part of Yaweh, and honouring them was therefore acceptable.

So in a round about way, the answer is yes, Romans believed in other cultures gods, often adopting them freely, but as facets of their own identifiable pantheon, and they were not above some pretty circumlocutious logic to make the narrative work for them.