I do this at ORD frequently. I try to return to Boston from Europe via ORD for the extra 3,000 miles when I have the time and the fare is available. Since legal connections allow plenty of time for checked bags but I don't usually have any, the scheduled LHR-ORD flight time allows for worse-than-average delays, and there are fairly frequent departures for BOS, I'm often in time for the flight before the one I'm booked on.

I get over to the domestic terminal as quickly as possible, clear security (using my boarding pass for the later flight, which I got at LHR), check the monitor for the next BOS departure and head for that gate. I've never been unable to stand by for that flight, and usually get on. On the rare occasion that I don't - well, that's why they have an AC.

FWIW, I'm always on the cheapest possible fare, often upgraded. Doesn't seem to make any difference one way or the other.