There would no doubt be lots of borrowed words, just as there are Indian words in English (bungalow for example)
If one assumes Rome has gone off and created New World colonies etc, then its come into contact with other language groups including Iroquois, Aztec-types, and of course Chinese
Best Regards
Grey Wolf
Indeed. No doubt you would see many borrowed words from Chinese, Greek, Amerindian, and Indian languages. And in turn you would see many Latin borrowed words in Chinese and Greek.
Here I'm assuming that the long-term success of Rome butterflies China, too, on the "millennial superpower" ongoing success path, which is the by far most likely TL.
India, ITTL, is a wild card, it may or may not be butterflied into lasting unification and being the third superpower, or become a fragmented buffer zone between the two giants, or be partitioned or absorbed by either, most likely Rome; if India gets its own imperial success story, we would see an Hindi imperial lingua franca emerge, and hence a fourth global imperial language.
It is also possible that Roman (or in a much, much less likely case, Norse) colonies in the Americas may break off and follow a USA-like path to be yet another global power, but again the differences between "Eurolatin" and "Atlanticlatin" would be just as marginal as British and American English. Moreover, another theoretical possibility (slightly more likely than a Norse America IMO, but still definitely improbable) is that the Norse manage to create their own empire in European Russia (but it is improbable because it is most likely that a successful Rome would eventually absorb the area) which fails or does not bother to absorb, and this would create another great power with a different Germanic language. Not in the same league as the 2/4 real global powers, although.
It is also possible that some East Asian "minor" civilization (say the Khmer or the Japanese) manage to avoid absorption or vassallage by the Chinese, Romans, and Indians, and pull a Meji to become a sizable medium power in their own weight. But in the un-Balkanized world created by Rome's survival, they would remain lightweights. IMO long-term success of Rome dooms Persia in the long end: sooner or later an empire that can pull on the whole resources of Europe and the Mediterranean manages to crush and absorb one that can rely just on the resources of the Iranian plateau, and controlling the latter is just too precious to control the trade flows to China and India.
Last but not least, I deem the possiblity of an Amerindian Meji really close to ASB. Their technological backwardness vs. Eurasian empires on a Renaissance stage wuld be just as damning as IOTL, they would be relentlessly conquered and absorbed by expanding Eurasian empires even more efficiently than by OTL conflicting European states (even if Rome and China would surely practice assimilation and not genocide, although they would surely find Aztec religion abhorrent and ruthlessly suppress it).