Hmm. I will be surprised if they install the OS, it costs money and they will expect you to have your discs.
As for just getting the upgrade disc, I don't know what it would do if you try. I suspect you will get a message saying you need 10.5 installed first, so you may have to buy a complete pack, or go a-hunting for them thar discs.
I would think it depends on where the Mac is being repaired. If it is an Apple Store, wouldn't they reinstall the OS as part of the repair? Especially if it is under an Apple Care warrantee.
As for the Snow Leopard Upgrade DVD: Yes, it will install the OS on a new disk.
I bought the Snow Leopard "upgrade" for $29 at the Apple Store. The "upgrade" went fine, and just for grins, I installed the OS on a 16GB USB memory stick. It uses about 11GB of the memory stick, and now I can boot my MBP from the USB stick.
BUT: There is no iLife software installed! iLife is included with a new Mac purchase, and you get the iLife CD & the OS DVD - but if you lost the CD / DVD set, you are screwed. You have to buy iLife & the OS.