He does this on-stage, as would most stand-up comedians who do voices. However, he regularly mocks it too. Also, the only voices he can really do are Sean Connery and James Mason. Which he acknowledges as well.
Particularly amusing is that it is Eddie Izzard playing James Mason playing God, scolding Eddie Izzard playing Sean Connery playing Noah.
Jeff Dunham is an exemplary showcase of this trope, what with being a ventriloquist and all. Epically lampshaded by Peanut in Spark of Insanity, after Peanut jokes about the pronunciation of Jeff's name:
Peanut: You know, the weird part is I am actually pissing him off. And he would like to kill me! But he will not because that would be a form of suicide!
Peanut also flat-out calls him on this during the appropriate-titled Arguing with Myself:
And of course, this has technically been true of every ventriloquist ever.
Michael Mcintyre has been known to perform conversations with himself on stage, often adopting different voices while doing so.
Mcintyre: I've been down there and it's not pretty, they're all wearing trousers, so we're gonna open with a skirt. Modelling it here is Scott. You alright, Scott? I'm alright. But you've got me in a skirt. I'm not happy about that yet.
In the comedy miming duo The Umbilical Brothers Shane often does all of the voices - including David's, who will often simply mime - and all of the sounds.