The Stack Overflow question "What happens when provision profile expires?" might be related this one.
The app will fail to launch due to the expired profile. The profile expires on its own, so I'd expect that the app does not "call home".
The same should be true when restoring from a backup.
The ordinary way to do what you want is to use MDM.
If you do not want your client to setup MDM, then the only way to do this is by adding a login system to your app. This way you can have employees of your customer install the app via the App Store using redemption codes, and then be able to stop them from using the app by invalidating their login.
Basically, no. You could put your app on the main App Store, publish it over TestFlight or have your client get going with an MDM.
There’s no easy way to side load apps aside from MDM so unless they jump through all the hoops to enterprise sign an app and you hand them the build, they need to get going selecting an MDM to push the VPP codes from the B2B App ...