I think the Chromecast uses whatever account the person casting is logged in with, things casted to other people's chromecasts show up in your history, so I'd expect to see ads if the person casting doesn't have Youtube Red. Also I don't see or recall associating the Chromecast with any Google accounts during setup so I'm not sure they have that information to make the link to allowing all videos played through a particular Chromecast to use the Red of the owner.

Mostly guessing though until someone tries it.