No.
And here is why:
Verizon was actually offered the iPhone first, before AT&T. They turned it down because Apple put too many restrictions on the deal.
-First, they would not allow Verizon to put their V-Cast music feature on the phone. In addition, they would not allow over the air music downloads (this has changed with the latest release).
-They also do not allow warranty exchanges at the store level, nor is the battery replaceable at the store level, both of which are very important to Verizon for obvious customer service reasons. Customers with warranty and battery issues have to send the phone to Apple for repairs, sometimes taking up to 2 weeks. Did I mention that you will be without your phone that entire time?
-In order to activate the iPhone, you have to take it home and connect it to your iTunes enables PC or laptop. It can not be activated in stores, also an important consideration for customer service.
-Finally, the iPhone is required to run on the slower
EDGE (comparable to Verizon's NationalAccess speed of approx. 80kbps) network, not BroadBand.
The other reason you will not see Verizon picking up the iPhone is due to AT&T's 5 year exclusive with Apple. No company in the US will get the phone during that 5 year contract term.