Yes, you add them, don't need to download them straight away and can download them 6 months later if you want as long as you have a PSN account. If you default on your PSN account, you lose access to the games so you need to keep the PSN account updated i.e. keep your PSN active. "As with all PS Plus games, you can keep and play them for as long as you have an active subscription."
https://www.ign.com/articles/playstation-plus-deal-get-a-year-for-3349
I add all the PSN games to my account, even if I don't intend to play them. My nephews/nieces/brother etc. might want to play them at some stage. I have most of the games/demos that came to PSN.
I play The Binding of Isaac Rebirth regularly, I got it on PSN in 2015(?), I love this game and even bought it on Steam to satisfy my need to play it if on PS4 or PC.