It is officially supported by CoG, but someone did report a bug with it a while back, so it is probably not entirely stable. (As of this writing, I was still able to reproduce the bug on the omnibus.)
Saving a checkpoint from the stats screen:
I don’t think this feature is officially supported by CoG, and I’m not sure what would happen if you tried to code a checkpoint save in the stats screen. Another HG author did raise this question, but I don’t think anyone was able to answer.