It is absolutely for sure E-V13 did exist among classical age Peleponnesians, the question is just which subclades and frequency! Because Psenichevo, the main Thracian group, directly to the North, covering a portion of modern Greece, was packed with E-V13. And we know that the Greeks mixed with Thracians. Historical Greek people had Thracian fathers, Thracian soldiers were mentioned in various armies and cities, and they were common among the Greek slaves as well. This means there is practically no way V13 was absent from classical Greece, including the Peleponnese, but it could have been fairly low. That's possible, a very low percentage and that almost none of the old lineages did survive into modernity. E-V13 was definitely picked up and incorporated by Slavs at different stages, from the Proto-Slavic to the Balkan Slavic stage. So they picked up E-V13 constantry, from starting point to destination. This means that they too brought a lot of E-V13 to Greece, presumably.
Its even possible that more of the classical era E-V13 survived in Anatolian and Cypriotic Greeks, as well as Southern Italians, than in modern Northern Greece. Because V13 is not V13 in this context. Its the subclades which really matter, since V13 was present since about 1.300-1.000 BC in Greece, but some lineages died out, others came in with different people. Just like R1b is not R1b for the Germanic vs. Celtic context, comparing e.g. U152 vs. U106. The same applies to some subclades of E-V13, but the problem is its timing is much shorter, and the original expansion involved all major lineages, so we really have to look for more recent subclades to know. In this case, early Greek and Thracian lineages in Greece should have no TMRCA with obvious Albanian, Vlach and Slavic lineages after 0 AD or better earlier. There are a lot which meet this requirement, but that's probably just because the sampling is insufficient. If it holds, there should be Greek lineages with no more recent TMRCA with other Balkan groups, but only Anatolian, Cypriotic and Southern Italian matches after 0 AD and preferably a last common ancestor even earlier. Ideally from the first expansion phase up to Hallstatt, so no later than 500 BC.