@gantoine, The simple answer is yes, a visitor is tracked by the affiliate software whenever he/she lands on your site following an affiliate link. The plugin will know if the visitor was referred by someone in the first place even if he/she returns to your site after a few days (this time is adjustable) to make payment.
The pre-approval part however is not built into the plugin so this is something you will have to manage. One way to do this without modifying the plugins would be to keep the pre-approval part separate. so you send your prospective clients to a landing page where you have a registration form (any contact form plugin will do) that they fill in for approval. once they are approved you tell them where to go to pay for membership.
1. The visitor lands on your landing page (they may have followed an affiliate link in which case they are tracked)
2. The visitor fills in an approval form (once they hit submit you get an email with the details)
3. If approved, you reveal the link where the visitor can go and make a payment for the membership (when they pay, the plugin knows if the visitor was referred by an affiliate in which case it will be tracked for commission purpose after sale)