No, Online Sales Pro does not allow customers to change their referrer to the system. OSP doesn't have sponsors.
So, how does the tracking work?
Affiliate links are embedded to track subscriptions with the aid of cookies. Cookies are small files which are stored on a user’s computer. They hold modest amounts of data specific to a website. For the tracking, the last cookie wins. Based on the browsing of the user, the subscription credit is provided to the last affiliate link used before signup.
Note: Only certain plan types are eligible for the Online Sales Pro affiliate program.