I would trust the rust compile/rerun process a lot more than an auto-updating linux distribution, personally. Sooner or later that auto-updating package manager will break your config file, itself, or both.
So that's not a problem. Besides the majority of nginx setups don't rely on too fancy things; most of the stuff that gets changed in updates that affect config files are the fancier nginx modules.
If you're following that approach then having auto updates enabled is kind of irrelevant/meaningless; at some point you're going to be running a very old (and unsupported) version of your distro with all that that implies.
Maybe. I have more faith in a Rust library to maintain API backward compatibility than a Linux distro, is what I'm saying.