Well, you can't make any ninja to perma stay via invite, because you can only invite ninja who are not in your home, so at best every other day.

That said, inviting doesn't "kick" people out. All uninvited ones show randomly. So even if you don't invite anyone, ningendo might not show up the next day.

And finally, 3 invites are ptw isn't it? I think it's a medal perk.