They won't leave the package (Apple requires signature). So there is that.
I have previously called when I had trcking info (on certain things, never an iPhone). As long as it's not yet out for delivery, they have always been able to work with me. I order a lot of saltwater corals, fish, etc. so I want them sitting in their overnight back as litle as possible. I always call in to where I know the package will be dispatched (last stop before delivery) and make sure they hold it for me. My local location is open by 8:30 am.
One caveat is that it needs to be a distribution location. It can not just be a "UPS Store".
It can indeed be picked up at UPS store, and is probably the best option for the OP:
http://www.ups.com/mychoice/features/
Hold for Will Call - Request packages to be held for pickup at a UPS facility.
Deliver to a UPS Retail Location - Request your packages be delivered to The UPS Store near you for pickup. ($5 per use for members, unlimited for Premium)
This is the assumption that it ships with UPS, although Fedex has a similar service:
http://www.fedex.com/us/delivery/
Customize Delivery Time
Deliver to Another Address
Hold at FedEx Location
Sign for a Package
Provide Delivery Instructions
Request Vacation Hold