Will a nandroid backup save me from a bad upgrade?
An update might include a new radio-firmware (see: What is radio firmware?; basically you can think of it as the "hardware-layer" or an API to give the installed (Android) system access to the hardware), which is not included with a Nandroid backup. It could also include a "recovery-image" (see: recovery-mode), which you did not include with your backup.

For the latter, you could simply include it with your Nandroid backup. The radio-image is a different thing: I know of no method to extract/backup it from a given device. You could, however, check which radio version is currently installed with your device, and see if you can get a "RUU" (Radio Unit Update) specifically for that.