Hey, another italian
So, regarding your question, you can make your private match "Public" so that the stats stick to your account, BUT in order to make people join your session from the "Play online" option you actually have to join yourself a playlist.
If you don't look for a game on the playlists the matchmaking server don't even know that you are running a match, so your host won't be sent to the people looking for a match... A bit confusing?
In poche parole, no LOL.