The Romans had lots of trade with India, to the point that Senators lamented to drain of silver from Rome to buy pepper. There is no reason some Indians couldn’t have followed the trade goods into the Med.
Yes, I believe you’re right.
There’s always another middleman to be cut-out if you’re just willing to go a little bit further on your trading expedition.
One can only imagine the expense of the stuff in that era with fairly primitive maritime technology and unfriendly states in Persia.