Yes, if you get Codecademy Pro then you’d be able to claim the certificate. You may need to go into the course and press “Next” at the end for it to trigger, but you’ll get the certificate without having to take the course again. Edit: As @codeneutrino pointed out, you would need to complete any projects and quizzes in order to get the certificate.
Once you unlock the certificate and it shows “View Certificate” on your profile, then the certificate will stay unlocked, even if you let your membership lapse after that.