That depends entirely on the model of each phone and how well equipped the store is. Assuming they have the right equipment, it should be possible as long as both phones are fairly recent models, but some older phones just don't have the capability.

just a sidenote, if you bought music from verizon's vcast music store from your phone, the version that is on your phone is locked to that phone, however the version that verizon allows you to download to your computer is not locked to a specific phone, however it still has drm...and my store has a ume36 the top of the line phonebook transfer/content transfer machine and it usually will only transfer pics/ringers/etc. if the phone is an older model as verizon didn't block access to the file system in the older phones...of course there are other ways of getting the info off such as bitpim and the like...really just depends on how much you want to work for your content