I honestly can't find (Game Mode game value). Since I can't find it and I've never used it, I can't know for sure but first of all my guess would be that it will work since hosting a game is not automated match making.
This said, I don't think it will work. Trigger stuff like that are usually for blizzard maps only.
Also, generally I wouldn't use "Not" like that. You should be able to change "==" into "!=" which means "not equal to". This should have the same effect.
and an automatched game is where you join a game automatically but it is created by blizzard, not by a normal creator, this happens when you try to join a map and there are no games available, a game is created and you are automatically host, but that is an automatically matched game, if you host it, it is a public game when you change it to open to public, and private before
I do know this - xenforo dropped the ball by not keeping the vbulletin reputation comments as a feature. The loss of the Reputation comments data when we switched to Xenforo really was the death knell for the site when it came to all the users that left. I know I missed it so much and I got way less interested in the site when that feature was gone and I run the site.
I'm on a page about incorrect corrections, and spent the better part of like two hours trying to get someone to understand that -5^2 = -25, not 25, and then that post had comments get reposted because that group is self sustaining, and that person was in turn trying to explain what I just explained to them. And I'm taking that as a victory