Right now, webpages can request information from the server whenever they want, right? So a pop-up or other annoying action could be taken at any point when you are viewing a webpage, yes? The only difference with this would be that in this case the timing would be server initiated instead of client initiated. From the user's perspective I'd expect there wouldn't be a noticable difference. It's still a webpage requesting information from a server, then processing and displaying that information for the user.
Of course a major difference would be making such intrusive actions easier to implement, so I won't deny that those potential implications are real.
I can see it making things like Gamecasts less network intensive though, perhaps making it easier to do stuff like that over phone networks or whatever, I dunno.