All data from public chat rooms should be available in the data dumps and queryable in the Stack Exchange Data Explorer. Of course, deleted messages should not be available (since the general public doesn't have the ability to view contents of deleted chat messages). Mod only and any other private / non-public chat rooms should also not be indexed, for obvious reasons.
I am aware of Why is chat.stackexchange.com not exposed in Data Explorer, which asks why the data is not there. This is a request for that data to be there. If there was an answer from staff, then perhaps a rationale for not including it could be seen as an implicit way to decline this request to include it. Until staff either explain why the data is not available or explicitly decline this feature request, I don't see why this should be closed as a duplicate of that question.