The current CCLI leaflet says this:-
Am I free to use Copyright Control / Author Unknown songs?
NO. CCLE cannot give permission to reproduce words of these songs because the owner cannot be traced. If you reproduce these words it is at YOUR OWN DISCRETION, and you should be prepared to pay royalties for that use, should the owner become known.
Note that thei comment relates to whether or not the CCL license covers this reproduction - it does not. And therefore they are making it absolutely clear that choosing to deal with Copyright Control / Author Unknown songs is not something they legislate or deal with. It is totally up to us as users.
Quite probably, especially if the author is long-dead and their Estate shows no interest / awareness, then it'll all be fine. But be alert to the fact that reproducing these songs is done at our own risk, and we cannot say "But I have a license."