I work for Best Buy Mobile...and the service plan that covers the Droid covers spillage, but not full submersion. If it gets dropped in a tub, or a pool, we'll check for water damage. It'll get sent in for service and if the internal indicators show submersion, then they won't be able to cover it. The only thing it doesn't cover as mentioned before is theft/loss.
I had an EMT bring me a blackberry curve the other day in 6 pieces. Her ambulance drove over it. We replaced it with a brand new phone and she got a new service plan on it since the old one got fulfilled with the destruction (massive) of her BB.
Whether Verizon will check for water damage...that totally depends on the competence of the people in that store. Some are great...some ain't too bright.
Like it was mentioned earlier...get it in writing. If the person that sold you the phone said that...it won't be honored...