Pretty much, yes. Although most of the guides install nix via curl. You can find the recommended installation procedure on the official nix website.
What I’m right now also realizing is that i switched things up. nix-shell -p curl creates a shell with the curl command temporarily available. If you exit this shell it’s gone. I use this all the time if if i don’t want to pollute my system with programs I only use once. If you want to permanently install something you have to use nix-env -iA nixpkgs.curl. But don’t take my words for granted, since I have never tested this on a non-nixos machine.
Note: You can also see how to install something by clicking on the package title in the nixpkgs repo.