If I delete an account on my PS4, would all the games downloaded on that account be deleted as well?

I have FIFA 17 bought on Account 1, but I've made Account 2 to prepare for FIFA 18 (I just change my account name every year).

It's still a month away, so I'm using PS+ from A1 to play online on A2. I don't need A1, so if I delete it, will FIFA 17 also be deleted? If not, could I buy PS+ on A2 and play FIFA 17 online?

Thanks!