It would but I have just seen that the sync speed is 1/180th. Whilst it's not end of the world it's not always great spending more money and getting a worse sync speed than the 600d.
I think I really need to get my hands on the 5diii and the 6D and see which one really works for me. That and make sure I get these jobs!
Oh yeah, I forgot about the sync speed. Now I remember why I didn't like the 6D after I looked at it more closely. Good luck with whatever you choose!