Ooo, one of my favorite questions, and the answer is: yeah, a bit. Now there is a bit of a cop-out answer in which you can say that common people would be affected do to economic ripples, in the same way that the price of houses in Florida can effect the fate of a second hand bookshop in Portland. The Eastern trade was a major locus of investment for those who could and for tax extraction, both of which had broad economic effects on the daily life of those in the empire. It is one of the many reasons I dislike the idea of "luxury trade".

But I think the question you are asking is whether a common person would actually be able to directly use the products of this trade, and the answer is that, situationally, yes. The primary good acquired from India was pepper which is today is exclusively used as a seasoning but in Roman times had a far more diverse set of uses, including medicinal and religious use. Pliny the Elder records the prince of black pepper as four denarii per Roman pound (which is roughly equivalent to twelve ounces). To help conceptualize that in modern terms, a Roman soldier would be paid about one denarius a day, and from a different perspective Matthew 20:1 has farmhands at a vineyard working for a denarius a day, so we can roughly say that was a stereotypical "day's wages". Four days labor for twelve ounces of pepper seems a lot, but that is an absurd amount of pepper--the shaker in my cabinet has one. So to reconceptualize further, the amount of pepper in a standard shaker is roughly equivalent to one third of a day's wage. Or, because I am sort of on a roll here, given a 9-5 job at US federal minimum wage a pepper shaker costs twenty dollars minus.

Now, this is a lot for pepper when you think of it as a condiment, but what about as a medicine or a religious offering? In day to day life pepper was certainly outside of the budget of an average Roman, but it was available at a price that was reasonable for certain occasions.

The impression that Indian goods wasn't just for the elite fits the archaeology remarkably well. for one, the horrea piperata (pepper warehouse) in Rome is enormous, much larger that would be neccesary for merely the rich even given that Rome was a stop over point for other trade. And more strikingly, of the three pepper types mentioned in Pliny, black, white, and long, white and long are judged as both superior and much more expensive at seven and fifteen denarii per Roman pound respectively. But the pepper that has been recovered from Egypt and elsewhere is almost exclusively black, to the point where black pepper recovered from Berenike is recorded by the kilogram, while white and long pepper is recorded by the grain. So the pepper that was traded in significant quantities was also the cheapest one--if it was only destined for those who whom price was no object we would expect a little diversity.

So to sum up, pepper would have been expensive for the average person but given the diversity of its uses was by no means out of financial reach.

A lot of this are my own conclusions but Steven Sidebotham's Berenike covers the data pretty well.