I am not trying to detract from your thread, I just wondered what the community thinks would have happened.
I was kidding, and also in the end, I think Pyrrhus might have been able to stabilize Greece under Macedonian control, but he would have lost any chance to control the Western Mediterranean or maintain importance in Mediterranean Politics. I think it would have been a tremendous waste of Pyrrhus's tremendous talent. The again, a united Greece could have a major butterflies.
A more united Greece would lead to headaches among the Romans, I'd imagine. It'd be even worse for the Romans if Pyrrhus then acted upon his old alliance among the Illyrians and added them to his kingdom. I think it would lead to quite an interesting rivalry.
There are a few key difference between him and Alexander. Pyrrhus had heirs unlike Alexander, he had plenty of alliances, and all those under him would be greek in culture, and thus no malignant influences like the Persians had on Alexander (I mean malignant as in leading to downfall). Heck, I could imagine a small hegemony eventually stretching from Rome and Sicily to Ionia, in the lifetime of Pyrrhus.