redeeming\registarring game code

Hello, bacause of many many problams which are too complecated to explain here.. i might neet to completely remove origin and the sims 3 games from my computer and download them all over again, my question is, if that happens, I only have the refrence number, redumption code and registration code.. is that enouge for me to relode the sims 3 pets which i bought through origin? ( the email recording my purches was deleted..)