I'm all about recognizing and rewarding good effort. But i want to first see the effort before it is rewarded. If i get a phone call for the bike being ready to pick up, in the time it was expected to be ready, i'd make sure i put a six pack in the car and after taking delivery of the bike being happy about the work done i'd thank the people for their effort and give them the six pack (it does work and helps building the relationship forward).
In the case of the OP, the bike was supposed to be ready in 3-4 days. A week later not even a call to explain why is the bike delayed. I wouldn't walk in with a six pack, basically bribing/begging them to do their job as they said they would in the time frame they said they would. Reinforcing/rewarding bad behavior isn't conducive to long term benefits even though it may yield the short term goal. Sure you may get them to work on the bike right away and probably have the bike ready after a little wait. But then they'd do the same thing next time you bring your bike. At the very least I'd just get my bike out of there and start looking for another LBS.
How is the relationship going to work moving forward? how often should i bring a six pack to expect them to do their job? Would now beer/pizza become an intangible but expected component of my pricing?
Slippery slope, not worth the hassle IMO but to each their own.
Good luck