I flew into BKK from IST in F on Dec 7th and was the only passenger in F. I was the first one off the plane and was met by someone waiting for my with a buggy and was taken to the fast track immigration line but it didn't matter since there was no one there at all at any lane (my flight was delayed 4 hours and seemed like it came in with no other flights having landed recently). After immigration we got to the the baggage claim where my bag was the 1st one off the plane. Instead of having the Star Alliance Priority tags I had THY 1st Class tags on it. I think that from the time I landed until the time I got into the taxi took something like 17 minutes.
There is no limo service provided by TK in BKK.