Twitch isn't going to care.
Potentially someone at NCSoft could have your stream brought to their attention. What could they do about it if someone at NCSoft decided something needed to be done?
Are YOU okay with getting a cease and desist from NCSoft's corporate lawyers? Because that's about the extent of what would happen.
I'd be pretty surprised if NCSoft is completely unaware of Paragon Chat, especially since it gets talked about in the gaming blog scene a couple of times every year. It's not really a secret project (even if they probably couldn't actually put their fingers on Codewalker or Leandro's True Name).
Given the failure of MxM, I doubt that they care much about Paragon City at this point. Besides - Building a base is just moving blocks around. You're not infringing on their IP by stacking desks and bookcases on top of each other. If you datamined Red Tomax and recreated all of those missions complete to the original text, THAT would be infringing their IP. If you copied those models out of the game files into another game and used them as if they were your own original creation, THAT would be infringing their IP.
I don't speak for Codewalker or the staff of CohTitan, but I don't see that streaming base building is going to do any real harm (and probably somebody, somewhere, is already doing it without being as concernedly courteous about it as you have been here). I also don't expect it to do any great good either. I suspect that everyone who is interested in Paragon Chat is already using it. The various Facebook nostalgia groups and such like to mull over their memories but they aren't actually interested in playing something unless it's just like the game in their increasingly muddy memories.
