They should... but your experience at your Apple Store could vary
It is a fairly simple process and you can do it yourself with minimal time and energy
You have several different options, but you will need to put your old HDD in an external enclosure, preferably Firewire, but you can use USB
You will need to format your new drive you purchased
You do that by booting from the DVD (hold the option key when booting and select the DVD) that came with your computer or a retail version of Leopard
Using Disk Utility, you select the new drive from the left column
Select the "erase" tab and use Mac OS Extended (Journaled)
This will format your drive
Then you can install OS X from the DVD
Reboot into your new system (holding the option key again, select your HDD)
If you have your old HDD in a Firewire enclosure, you can use Migration Assistant
If it is USB, you can either use Disk Copy's restore feature
Or you can download Carbon Copy Cloner or SuperDuper and clone the old drive to the new Drive
It may sound intimidating, but it isn't really that difficult
The users here will be glad to walk you through the process as you have questions
Woof, Woof - Dawg