I dunno, there is a possibility, but I would like to think that Apple has realized this and tried to compensate, But they might be go super slow for a while...
I just think that it is a little risky launching 3 new services the same day. I think that Mobile Me should launch Monday 07/07, Software 2.0 either a couple days before or after iPhone. I think that this would make the iPhone launch day go much smoother.
It's not like iTunes and MobileMe are running off of the same servers. Everything will be fine, if not somewhat slower than normal because of the heavy traffic.
I wouldn't imagine it's an all of nothing thing. Demand will be heavy and have spikes, but what would it exaclty go down for? iTunes downloads? That's served by another company on behalf of Apple I think.