Honestly, this can work... But Super Dave426 is correct... It takes some effort to make it happen. First, you need Sprint to unlock the SIM slot and release the device. Releasing the device is the hard part - the SIM slot is a pain, but if you have Sprint service, they will usually try to make it happen for you in a timely manner. The problem with most of the Sprint call center people is that they have no idea how to release a device. If you get lucky, you'll end up with someone that has a clue. If not, you'll have to try this about 100 times before it works correctly.
Once all that is done, you'll need to have someone at Verizon add the device's IMEI/MEID to the Verizon system. Again 99.9% of the call center people out there won't have a clue how to do this, nor should they. It's a process of going into the device database and adding the phone that you are wanting to bring over. They don't make money on this and they would rather just sell you a new phone - or heck - even give you a new phone. Once VZ adds it to the database, it should take between 1-3 business days for the device to show up and let the activation happen.
Once you're there, you can do it, but you will still have to root the phone to get rid of all the Sprint bloat, and some features will never be available for outside devices. So, good luck!