Hi @anon96754910, I’m glad to hear your team is excited and wants to join your Organization in Asana! Unfortunately this is currently not possible, we have a similar feedback request and you can upvote here: Send notification to Admins when new user is added .
In the meantime, you can try sending a Team Conversation to all Team Members and add more information about why it’s important new members go through your Onboarding Program and to make sure they always assign a task to their Admin when they would like to add new Members or they can submit a form to request request! 
I hope this help!