Yes, that's correct, it's only about searching the right directories to find and execute the program you asked for.
But autocomplete after sudo doesn't work for me on a stock Debian install anyway, not sure what one needs to do to get around that. I don't really rely on it. If I'm doing enough work that needs root I start the session with "sudo su -" anyway so not having autocomplete after sudo is not a big deal for me.
