I think so... I've been with foreigners entering through T3. Frankly once you're at the airport its a bit of a fait-a-complis. If you have an onward ticket within the next few hours its unlikely they would put you on the next flight back - even if you didn't have a transit visa when you should have had one. One of the reasons for the transit visa requirement was because people were turning up in London and claiming asylum rather than taking an onward flight. So this precaution has been defeated once you've arrived at the airport. If your intention was to stay and claim asylum then they can't put you back on the plane anyway. So not much to lose by letting you continue.

In the UK I'm based in Croydon - and work about 100 yards from the Immigration office. Quite often people are let in with all kinds of paperwork deficiencies. Sometimes they are given train tickets to Croydon for further "processing" and just "disappear". (I've met them on trains down from Victoria to East Croydon. Some are quite open about their intentions.)

A Japanese I know was refused a normal visa at immigration. She had come to the UK to look for a job. Immigration realised this and permitted her entry for only 5 days. Basically enough time to recover, meet a friend and then return to Japan. To seek work was not a valid reason for entry, but still they showed some flexibility rather than put her on the next flight back.

As B747 says, a real issue is whether you can board the flight in the first place. He seems to be the oracle on this. I myself have occasionally had to fight it out at check-in when I've been within entry requirements, but check-in staff had an "overly cautious" simplified version of the rules and initially wanted to deny boarding.

One tip on the check-in problem is to phone ahead (the check-in rather than the airline office). Call them around the time check-in opens for your flight but on an earlier day and run your scenario past them. Check how they interpret the rules so you can preempt any argument.