Following the events in New York the military would indeed be very interested in a non-RT aircraft continuing (how many terrorists are familiar with transponder settings??????, we've just given them one here!). The Ukmil would be fine once they’ve positively established the intentions but the Americans would certainly be a little more anxious if not Gungho!
Regarding North Atlantic Clearances, they can be obtained on the ground (Prestwick) and by data link so it is possible that a non-RT flight could conceivably cross the pond.
However, given the vagaries of the Eastern Seaboard weather at this time of year and the heightened security procedures I would definitely call a captain’s decision to continue into doubt, after he gets out of an American jail if their military haven’t shot him down.