From our experiences, SteamCMD is semi-supported: We're downloading/updating/verifying AMS via SteamCMD (dedicated server app, anonymous logon) and that part works just fine.
However, the Steam server list integration seems to require the full Steam client to be running (can be offline, so I reckon it's some API usage via DLLs not included/compatible with SteamCMD) - so you'll always have to have both, SteamCMD and Steam, running in order for the server to be properly listed. While this seems redundant, its advantage is you won't have to switch on/offline with the full Steam client in order to update the dedicated server app itself as you can do this through SteamCMD scripts.