It will if you don’t have offline maps.
The GPs position does not depend on data speed, but a precise dot on a blank screen is not so useful. 
This has NOTHING to do with being impatient. Follow along:
[ul]
[li]I fly in to a new city.[/li][li]I get to the rental car lot.[/li][li]Get in car, start it up, tell my GPS device where I want to go. This can be a smartphone basd GPS or a dedicated GPS.[/li][li]But wait, I’m under a metal or concrete cover, so no GPS signal.[/li][li]The moment I leave the rental car lot, I have to go left or right, so I need GPS to be working now, not later.[/li][li]Ah, they have thoughtfully provided a parking area over there that I can pull over to, and let my GPS figure out where I am. Yay![/li][/ul]
Had this exact scenario play out when I flew into Heathrow and rented a car. From the covered area where my car was to the front gate was covered by a metal canopy the entire way. No GPS waiting area. Had no idea which way to turn when I got through the gate. I guessed left, and (of course) was wrong.
It wasn’t that I was in a hurry. It was just that I needed to know which way to turn. If I had taken an earlier flight, I would still have had the same problem, just would have had it earlier.
My first GPS unit, a Magellan, had a spot you could press on the setup screen to say, “You’re no where near where you were when you went to sleep.” My present unit, a Garmin does not have this feature. On both of them it’s about five minutes to sync up if it had been moved a large distance or been off a while.
Is it any faster on smartphones, which have other (usually less precise) ways of determining location? A phone always knows at least which cell it’s in, which, while not precise enough for navigation, should at least make it a lot easier for the GPS to zero in.
Smartphones can make use of Assisted-GPS, where they receive details of their current approximate location and crucially the current satellite configuration through the network they are attached to. Standalone receivers only have the data from the last time they were used and must download current data from the satellites themselves. This can take a very long time if the receiver has only very old data to work from.
I’ve never seen it, but excellent idea. It seems especially the add on GPS systems you’re more likely to use in a rental car take a few minutes get their bearings, and won’t do it inside a parking garage. You can usually figure it out the old fashioned way by asking or signs which way to head initially in an unfamiliar place, but it’s nicer if the GPS just tells you.
You might have your phone do it off wifi/cellphone signals as you walk to the rental counter, except maybe if it’s a foreign country where your phone doesn’t work or you don’t have a smart phone, and personally I have one but am not accustomed to using the map app, extremely fast battery drain if I do for one thing. And while the phone will work at most airports, I found on an extensive drive around the US last year (starting with add on GPS not yet working when I left the rental garage at SFO) that there isn’t sufficient signal or data rate (AT&T) to navigate by phone in lots of places.
But if you are close by or even behind them, shouldn’t you have the same ability to synch?
I’m sure the satellite people have some way to make sure that all of their access couldn’t possibly be bogarted by just one minivan…
Yeah, a lot faster! As ticker said, they use assisted GPS but also wifi positioning + cell tower trilateration + GLONASS.
Edit: No, smartphones are much better at acquiring an initial satellite lock because they have other means of helping them estimate a location, not just GPS satellites. They use all the signals in conjunction. It starts as soon as you exit airplane mode and start talking to the towers, before the GPS receiver is ever turned on. Also they tend to periodically ping the GPS software, even as you’re walking from the airport to the parking structure, let’s say, not just once you’ve started the car.
The GPS reception has nothing to do with nearby vehicles, but rather overhead obstructions like other floors or metal roofs.
Your message board GPS must not be functioning properly, because you missed the point by at least a mile.
Was the car rental depot that the OP encountered in a covered parking garage? In that case a separate GPS synching period in an open parking lot would make sense to me, but only then.
Personally the times I have picked up a rental car of a type that I have not driven before, synching the GPS is the least of my worries. I need at least a quarter of an hour to look up the controls for lights, wipers, where the tank cover is and how to unlock it, etc. - after a few terrifying times of driving into a tunnel or into rain and searching for the light or wiper controls, and a few deeply embarassing times sitting in a gas station with others behind me, leafing through the manual on how to unlock the gas tank.
I assume a lot of other drivers go through that period when picking up a rental, and in an open lot that time would also take care of booting the navigation system. So a separate open lot would only make sense if the car is picked up in a covered lot.