> but I would need to check each type to see whether it is actually saved or not

Huh, why? According to http://beta.musicbrainz.org/doc/MusicBrainz_Picard/Tags/Mapping %compilation% is written for all formats and https://github.com/musicbrainz/picard/pull/179 didn't change this. I'm just not seeing why TCMP needs to be mentioned specifically.