Until it doesn’t, as several users discovered last December (including me).
In addition to the “unsupported” message, an additional “unhealthy” message appeared. In my case, I was using Ubuntu 18.05 and Supervisor considered the installed version of Network Manager to be out of date (with no upgrade path). While in the “unhealthy” state, Supervisor disallowed upgrading Home Assistant and creating snapshots. The quick fix was to upgrade to Ubuntu 20.04 (which has an updated version of Network Manager).
All of this happened immediately after a Supervisor upgrade (which cannot be suppressed) and shortly before the Christmas holidays (when fixing one’s broken instance of Home Assistant isn’t a welcome task). After the holidays, I switched to the officially-supported Debian 10.