If you goto:
Control Panel » Group Management
you will see a note at the bottom that states:
By filling in the Post Count field you can make it so users will automatically be added to that particular group once they reach the designated Post Count. Leave blank, or 0, to disable this feature.
The post count field only appears for the most part for groups added that are not the default ones.
So if you add a group and set it to 100 posts,even if someone has a 1000 they will be added when they post 1001.
To invite them in would be another issue.
There would not be a automatic say welcome message.
but you could say add someone manually to the group and post a pm to them that states you are now able to post in x forum.
So in stock code no, There is not a registration for just a specific forum.
It would be a manual thing.
You could set the forum as a teaser forum so they see it exists but can't access it. Then have a note to request to be added to it.
There is a forum here called teaser forum that does just that.
