No. Verizon only allows pre-approved devices to appear on their network, regardless of whether you are prepaid or postpaid. They do this by checking the IMEI identifier of the device. If it's not one of theirs, it won't work.
Their network is also incompatible with the radio in this device.
Unless something has changed, the article you linked to is basically the end of the story. Despite promises, Verizon has not moved to permit the Nexus 7 on their network, and there is no easy/useful enforcement mechanism to make them do so. The provisions are effectively toothless.
If you read forum reports, it seems people are activating it by using IMEI numbers from other tablets and whatnot, but Verizon is not making it easy, or (IMO) living up to their contractual obligations.
TMobile has some really good plans. They are trying a lot of new things. An unlimited plan from them with a Nexus 5 is what I use and I'm very happy with it.
Thanks for this - that sucks hard, I'm sorely tempted to switch off of Verizon. The only thing that keeps me on there is that I'm on a $40/month legacy family plan that still has unlimited data.
Their network is also incompatible with the radio in this device.