It's not that I won't test it out - it's that I don't have the setup to test it out. ;-)
But, my answer still stands, in that, AFAIK Mainstage won't sync to incoming midi clock or send it out. I can't give a reason for that, only the Mainstage/Logic developers can do that ;-)
What I will suggest is that Mainstage is still at version 1. Hopefully future versions will support this.
As for Logic... well, Logic has been and is used live by any artists. Amongst them, Bjork!
It's very possible to use Logic live. You may consider setting up a template in Logic and create objects to control things in the Environment - similar to Mainstage, but not as pretty to look at!
You can do all the same stuff with UB triggering samples etc & sync PC Live to Logic too :)