Sanskrit is a pretty easy language to learn, if you can memorise a lot of words quickly. But by the time the Romans rolled in, Sanskrit was no longer the language of the masses. Only the priests and some of the nobles and mercantile class knew sanskrit enough to possible hold a conversation in it beyond, "hello! my name is..."
However since the grammatical structure of sanskrit and latin are very similar, translation should pose less of a problem.
As for medicine, you mean Charaka and Sushruta right? the famous indian physician and surgeon, respectively? They were both around before rome was anything more than a hamlet in Italia.
Finally Buddhism. I guess it was too alien to the Western culture to be widely accepted in the west in the absence of royal patronage.
hope this helps. Didn't mean to torpedo your arguments. Just was stating my thoughts.
As for the Indian numerals (why do people insist on calling it arabic anyways

) well i can't see how it will work without a zero. Can some one please explain how will they write '10' or a '100'?
I was referring to
cultural translation, not linguistic. Translating stuff from Sanskrit to Latin should be relatively trivial. Getting Latin readers
interested in what is translated (which is, of course, a requirement for the translation to be done) could be trickier.
I mean, the Paninian tradition has really deep, impressive understanding of how the Sanskrit language works. It can be translated into Latin (it happened IOTL in the Early Modern era) but why would an Aristotelian thinker in Rome about 250 AD even come to care about Sanskrit? They didn't seem to have thought that there is something interesting to be learnt by studying how languages function.
Indian thought had (and has) this very interesting notion of
shabda, usually rendered as "knowing from words". That is, the idea that words are able to convey some useful knowledge is seen as epistemic problem worth discussing in Indian philosophy. It seems that it was never an issue in Classical Greaco-Roman philosophy. They were interested in the persuasive power of words, and they needed descriptive, didactic grammars of Greek and Latin, but they did not appear to have thought of language of something calling for
inquiry (logic is another matter though). This means that a lot of Indian thought involving linguistic, logical and epistemological problems would likely appear utterly uninteresting to the average philosopher in the Roman Empire.
Now, I don't think it is impossible to change that. Perhaps some serious Indian mathematics is introduced, or, better yet, some Indian logic finds its way into narrative texts that are translated for entertainment/instruction (mirror of princes or the like) via Persia (where they appear to have circulated). Somebody in, say, Athens feels like it's worth to know more. If some thinkers on the Roman side spark a debate where Indian texts/concepts become relevant, they might to want to have more of it, generating a translation current.
Logic is the most likely beneficiary, together with maths and medicine.
I guess that in maths, you may get an earlier departure from the largely geometrical approach of the Classical arithmetics into a more abstract outlook into things like number theory. That could have a huge impact.
Algebra might have a big headstart.