There actually seems to have been comparably active Buddhist activity in the Eastern Mediterranean, especially in those areas such as Egypt, the Levant, Asia Minor, and Greece, at least during the 1st century BCE and beyond.
For example, there have been Buddhist gravestones from the Ptolemaic period found in Alexandria, adorned with the Dharma wheel. There are Roman accounts of an Indian ruler sending an embassy to Caesar Augustus, with this embassy being staffed by a number 'sramanas' (Buddhist ascetics and preachers), one of whom supposedly immolated himself in Athens to demonstrate his faith in a widely reported incident. There is also evidence of correspondence between Emperor Ashoka and Ptolemy II Philadelphus, and that the two sent embassies to each other's courts a number of times; correspondence between them points to the presence of Buddhist monks in Alexandria. Some historians speculate that there may have even been a Buddhist (Theravadan) monastic order in Alexandria in the first century CE.
The question is: how likely is it that Buddhist thought influenced Gnosticism? Or even Christianity?