I will include a rather lengthy explanation, which might be unnecessary for users familiar with the stuff I describe. Therefore:
TL;DR: Per-site-metas can have chat rooms associated with them, too. Are they shown in the side-bar when viewing the questions?
When viewing a questions, sometimes chat rooms are shown on the right in the side-bar. It might look something like this:
(Maybe you can see something similar while you are viewing this question.)
They do now always appear there. They are shown when viewing both questions on main and questions on meta. I do not know how the rooms are selected, but it seems that usually they are rooms which were active not too long ago. When I tried it now, on both main and meta I saw rooms associated with the main site.
I learned that some per-site-metas have also rooms associated with them from here: http://meta.math.stackexchange.com/questions/18990/mathematics-meta-chat-room. There are not many per-site-metas which have chat rooms. If we do not count meta.SE, which is not a per-site-meta site, then I was able to find such rooms at meta.gaming.SE, meta.matheducators.SE, meta.math.SE, meta.mathoverflow.net, meta.SF, meta.SO and meta.SU. I do not know why only some meta sites have chat rooms.
One advantage of these rooms is that for every site (which includes per-site-metas), at least one room is always left. I.e., it is not frozen even if it was inactive for 14 days. The users usually do not create rooms associated with a meta site - you can see that in examples I have linked above only one room is associated with each of those meta sites (at the moment). So unless other rooms associated with the same meta, these rooms will theoretically exist indefinitely.
Perhaps such rooms could be put to some good use. But there is a question whether users will notice them. I guess that typically when users go to chat, their view rooms associated with the site they were on. The rooms associated with meta are not shown there. So will users notice existence of a room associated with meta somewhere? This brings me finally to the question:
Are the rooms associated with per-site-meta shown too when viewing questions on main or meta? Are they perhaps shown in some other places I did not notice?