Yeah, it works great! Odds are you might have some libraries that are open to everyone in your county or even your state (assuming you live in the US, but I don't even know if or how Libby would work elsewhere). There are also libraries that are open to anyone in the country, though they seem to be closing that option. And there are some libraries that will give cards to non-residents for a recurring fee.

...and you didn't hear this from me, but you can also, you know, lie. Use a realty website like Realtor.com or Zillow, get a valid address, and sign up for some libraries. Very rarely one will check your IP, but otherwise, you know. I haven't had to do it because I'm spoiled as a New Yorker, but it's an option.