Does the URL your PPV traffic software is hosted on matter when it comes to conversions? For example, lets say I have Prosper202 installed on myultrasupertrackingdomain123.com. When someone gets a popup from a PPV network, do they even see that domain name? Now if that domain name actually shows up, do you think conversions would improve if I had a domain called mybestoffers.com etc.?
^ yes. I've seen a thread that covered that, use the search function. But in addition given that my original background is domains I can assure you that using good domains helps conversions for sure 
But really, it does help to have an "offer" related domain? I'm trying to think of it from the user's perspective. I have the word "track" in my domain and I think that some users might be paranoid if they saw that word in the domain and would not engage the popup.