Driving from the Carolinas to New York City, would taking the Chesapeake Bay Bridge Tunnel save time?

I haven't tried the bridge/tunnel at all, but I agree the traffic in DC is horrendous, so it may well be worth your time if the bridge/tunnel isn't out of your way to get to. A note about Philly though, since you're going for NYC, you might consider getting off 95 just before Wilmington onto 295, cross the Delaware Memorial Bridge, an take the NJ Turnpike around Philly. It'll most likely be quicker than taking 95 or 295, especially if rush hour. And the Turnpike blends into 95 north of Philly, so you'll end up on the same track heading into NYC. Only note of caution is all the long distance truckers do the same thing.