My experience talking to both verizon sales reps on the phone and in chat says otherwise. They both told me that the only damage protection that verizon will sell (and the preorder of the iphone 4 8GB agrees with this) is the Assurion one that they offer you and that in order to get Apple's damage protection you will have to deal directly with Apple(note this is different than Sprint). Did you ask specifically about applecare+ and make sure that he wasn't talking about the monthly charge insurance that verizon sells?
After some discussion with verizon reps we concluded that the only way for me to get what I want(Iphone 4S with Applecare+ as a new line on a family plan) without physically going to the Apple store on launch date was to first add a line with an old phone to my family plan (adding a new person with an Iphone 4s) and then tonight upgrade that new line to an iphone 4s.