I would like to get The Binding of Isaac for with this months PS Plus membership. However, I don't plan to purchase a ps4 until March. Could I buy a PS Plus membership, go to the playstation store website, and secure my purchase of the free game without actually owning a Sony console yet?
Yes, I'm pretty sure you can. I can confirm that this worked for my PS3 and PS Vita, I created subscription before I bought them. I would assume that whis works same way for PS4. Actually it works, I can do purchases of a PS+ PS4 games, and they are in my download list, it's just that I can't be 100% sure yet (but I'm 99.97% sure ^_^).
I have managed to do this for various PS4 games on the PSPlus service, and they appear on my downloads list.
The option is available to download Pix the Cat or Dust: An Elysium Tale despite them not currently being available on PS+ or previously downloaded. I did not have a PS4 at the time of "purchase".
I have also done this with my PS Vita, as I ended up without a Vita for a few months. I have successfully downloaded games that I got on PS+ and had expired since.
Unfortunately no, you can't. I discovered this when I used to download every single "free" psplus game and pause the download until I wanted it, in the hope it would stay there forever. If you haven't downloaded the game fully onto your playstation before it gets removed from psplus games list, you can't download it.
By the way, as some people have recently downvoted this answer... the PS Plus scheme has changed drastically since I originally posted this. You can now just press "add to library". so this answer is now irrelevant.