I'm not an expert, since I usually terminate in Dulles. You might try asking on flyertalk, but I do suspect that 7 am is not peak arrivals period. Most of the Europe flights arrive in the afternoon. I do know there's signs pointing a different way for connecting flights. In an ideal world, that would take you to a place where they'd be interested in moving you along quickly, but I suspect it just takes one customs official who looks at you funny to mess everything up...

On the other hand, if you're arriving that early, you should have a lot of options for later in the day in case you miss your flight.