No is the short answer. Although a few continuation cars have crept in under the radar, they do specify original cars only. Although Richard Mille's T70 always seems to get an entry and that wasn't built until the early 1980's......
Notin the actual racing, however the GT 40 Enthusiasts club have a half hour session on the track on the Friday evening. Full track, fully marshaled and as fast as you dare. You need to sign indemnities etc and pay the fee about £300 from memory but thats the quickest way you will get on the track.
Full details are on the club website and forum section.
I know of no cars which are not purported to be genuine taking part in the actual racing. I suppose it's possible that a Gelscoe car might be accepted, but I'm certain the organizers would not knowingly accept a 'kit car' even if it was to the high standard of Superformance.
I've heard rumors of big-time Euro vintage racers setting their genuine cars to the side and campaigning perfect copies, but I've yet to see anything to substantiate those rumors.