I started with a cup a day from 32 weeks, gradually increasing to about 3 cups a day. Waters broke at 11pm on due date and had her by 3.30pm the next day. Active labour was recorded as 7 hours and pushed her our in 10 mins! Hard to say if tea helped but felt like I had decent not too protracted labour (and I had an epi later on which slowed things down a bit). After my waters broke though I have to say there was no gradual build up of contractions - they started within the hour every 3-4 mins lasting for a minute - I wonder now whether tea did make them more efficient!
Oh this is true for me too, I didn't really get a build up to labour, I got some twinges in the day to suggest it was going to start but they weren't painful, but from my first proper contraction they were pretty full on and every 5 mins right from the start and then just got closer together until he was born 4 hours later, so yeah although mine was a short labour it was pretty intense, and I guess "efficient"!