uhhh... not trying to be mean, but you should proofread. to answer your question, they should NOT know, but that doesn't mean that they CAN'T know. if you are caught .... somehow.... you might face a huge bill. chances are, you have at least one market app that tracks your internet usage and has the ability to report your usage to google, verizon, motorola, or any huge # of advertising companies. many apps even "come alive" without you having to launch them. be careful what/who you give control over your phone privacy. each app is supposed to outline what they can/will control by you downloading it.
that being said, you are allowed to put any U.S. legal app on your phone and use it. verizon can not disallow you to use the device that you rightfully own. they can, however, cancel your contract and/or void your warranty for misuse.
They have absolutely no way of knowing if your tethering if you used PDAnet, unless you are pulling some huge GB down but even then they have no way of knowing. When the official tethering support comes out then they will know if you use it, not with PDAnet though.