Does a relief pitcher who allows inherited runners to score receive a blown save?

I don't think it's a save situation if a pitcher comes in with runners on...

But even if it is, then it is indeed a blown save. He gave up the run even if it is unearned. He was expected to close the game out / earn a save and he blew it.

Yes he is. His ERA wouldn't be affected, but if he gives up the tying run under any circumstances, he is charged with a blown save.