Shops vary widely, but my goal is to get the bike built & tuned the same day it arrives, or the next day at worst.
1. the sooner the customer gets it, the happier they'll be, and the more good word-of-mouth we might reap from it. Win-win
2. the sooner I start on it, the sooner I'll know if there's some kind of show-stopping problem with the bike (blems, defects, shipping damage, etc) and will have that much more lead time to fix it and avoid disappointing the customer.*
3. if the bike's only partially paid-off, then the sooner we get it to the customer, the better for our cash flow situation. Carrot... stick... yeah
*This is also why I discourage our sales guys from giving out tracking numbers, or telling the customer the bike's arrived and will definitely be ready by such-&-such time of day. I'll refrain from specific horror stories, but let's just say it can end badly 
At a typical shop, the actual build-&-tune process is likely to take 1 to 1 1/2 hours depending on the bike and how far into quality assurance they go. Where I work now, we have a QA procedure and checklist, and lean towards proactive prevention of foreseeable issues, so I usually allocate 90-120 minutes. An older version of the QA sheet's attached if anyone's curious; just doing all the torque checks and QA checkoffs is 10-15 minutes' worth of work.
Going back to the main topic, I suggest simply asking your shop when to expect the bike to be ready, not whether it's arrived. They know the expected arrival date and their subsequent lead-out time, and should be able to give you a solid answer.