No, ThirstyAffiliates is the wrong tool for that job.
ThirstyAffiliates is a plugin for your affiliates to manage their affiliate links from all of the affiliate programs they belong to (including yours).
It is not a tool for store owners to run their own affiliate program.
A great tool that will let you run your affiliate program for your store and is integrated with a number of platforms is a plugin called AffiliateWP.
You can download it here.