Is "Ignore ownership on this volume" reversible? In other words, does it just hide the permissions on file, or change them? More specifically, if you have a volume with file on it that have different owners and you check Ignore ownership on this volume, and then later you uncheck it, will the original ownerships/permissions revive correctly? 

I have not seen anything that answers this directly, although what I have seen about problems with Ignore ownership settings needing to be reset and about them being recorded in /var/db/volinfo.database suggest that the answer to my questions is yes. Nevertheless, it would be very reassuring if someone could confirm this.

(The context is that I have a bootable backup on an external disk that I would like to keep the permissions intact on so that I can boot from it if needed, but I would also like to be able to read from it on another computer where the users don’t match up to give me access to the relevant files. Being able to switch Ignore ownership on for the latter, and then switch it off again to leave the disk in good condition for potential boot/restore use, looks like it would be a nice, simple way of doing this, but I am concerned about breaking things if I experiment.)
Yes, ignoring ownership is reversible, but I wouldn't recommend that as being a solution to your problem because the Ignore ownership on this volume option shouldn't be used on a drive you also want to use as a bootable drive for one of your Macs. And, since your Macs are running different versions of macOS, you may be asking for added trouble. In addition, you mention that this is also a backup drive - while you don't clarify this, in the case of drives also used by Time Machine Apple recommends:


  Make sure "Ignore ownership on this volume" at the bottom of the "Sharing &amp; Permissions" section of the Get Info window is deselected (unchecked).


Source: https://support.apple.com/HT202380

Ignore ownership on this volume

The main reason the Ignore ownership on this volume option exists is to ensure that file servers, applications, operating systems, etc can still function correctly because they require permissions to keep track of which users have access to which files. 

However, drives used purely for data storage (as opposed to being boot volumes) shouldn't generally use permissions and ownership (although they can be secured in other ways). 

What I'm saying is that the Ignore ownership on this volume option shouldn't be used for boot disks or server volumes (and you may not even get the option anyway - depending on macOS version). It's best this is only used for drives that are used purely for data storage, and even then only for drives that are directly connected to your computer.