Yes! (kind of, I wish `nix install` was a thing)

    # search for a package called `foo`
    nix search nixpkgs foo
    # install package foo, user-wide
    nix-env -i foo

The CLI UX can get better, and I'm fairly sure folks are working on it.

You can also test-drive a package without committing to it, e.g. you want to try the program `cowsay` but only want to use it once:

    nix-shell -p cowsay
    cowsay
    exit

This spawns a new shell with `cowsay` available, and after you exit it won't be cluttering your system packages.