AI counts, yus. I only play qm/tl with a friend and he never plays so I play AI lots. It's a stress-free environment to level in and get a feel for some of the ones I'm not familiar with. Pretty sure that was all AI aside from the super fun pool brawl since I've been leveling lots of diff ones lately and I don't think he played last week at all.
Also:
http://media.blizzard.com/heroes/med...akes_Rules.pdf
See #4
Happy Summer