If you have a Verizon router and it's providing wifi coverage to the room where your smart TV is located, and if your smart TV has wifi capability, then yes, you should be able to connect the smart TV wirelessly.
However, what you might consider, rather than using wifi, is using an Actiontec adapter, ECB2500C:
http://www.actiontec.com/251.html
That adapter will let you easily connect your smart TV via Ethernet cable. (Assuming, of course, that your TV has an Ethernet port for its smart TV features.) You may find that the hardwired connection is more reliable and less subject to interference than is wifi.
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