We flew LAX-LHR in C and were excited to use our Fast Track invitations on arrival ... but this actually turned out to be slower than going in the regular queue.
When we arrived, the Fast Track queue had about six pax in front of us (waiting to talk to one agent), and the regular queue had zero pax (waiting to talk to one different agent). We ended up ducking over to the regular track.
(Not that it mattered, as our luggage was delayed for two hours!)