Thanks everyone--this is reassuring, as I certainly don't want to show up at IAD after 28 hours enjoying DC and being told that the rest of my carefully planned international itinerary is toast.

All experiences seem to be domestic, however--to be extra sure, can anyone out there confirm that they have had no problems doing this with an international, multicarrier Star award (though with UA flights on both ends of the attempted >24 hour stopover)?