No. Good question though!
The reason is that Ditto, even when transformed, keeps its species, Ditto. While it might copy form changes, stat boosts, nicknames, etc. it's still a Ditto in the end. And thus, it cannot Mega Evolve. (inb4 mega ditto is released and it's just mew)
As previously stated, though, you can come in on a Mega Pokemon and become them without having to Mega Evolve.