I had verizon for a matter of about 6 months and ran my server all that time. They never contacted me.
However, I know a guy who does support for them and he has explained that they rarely if ever check for servers unless you are consuming a lot of bandwidth all the time. In the event that they do check for the server, they will warn you that you are in violation of the EULA (usually by email) and then they will disconnect you if you fail to comply withiin the alotted time frame.
He too runs a server on the verizon network has had his server up and running for approximately 16 months without so much as a scan from Verizon yet.

Reason for not permitting the server : Unknown as of now. I have speculated that it is because of the manner in which the lines are leased and the amount of bandwidth the ISP's have at their disposal. When you lease your line, the ISP has to be able to provide x kbps of bandwidth for your line in particular. With the amount you pay for an entertainment account, they could making more money off of it by alotting that same bandwidth to a company that will pay more for the benefit of an always on connection and the promise of immediate support if needed. You ever notice how little priority an entertainment account carries?