I've seen other servers run this plugin with a setup where: Building is protected while online, and protected for X amount of hours after logging out. 
I do not have any reason to believe that they're using another plugin to manage online protection since the same popup GUI appears regardless of if the user is protected online or protected offline. 

Is there any clear way to make this plugin function as stated above or any way to have this functionality added in a future version possibly? 

If its not possible to achieve this with AOR, does anyone know if there's another method I could use to achieve what this does and simultaneously protect online with the same popup? 

This is the plug-in Anti Offline Raid
it does what it says, it protects players from offline raiding.
There are a couple of ways to cheat on this plugin, but I'm happy with it.

you have a few more options
https://umod.org/plugins/local-time-damage-control

https://umod.org/plugins/wipe-protection

Unfortunately, this does not accomplish what I'm looking for.
I just want the protection to remain active while the player is online, and then have the 48-hour raid protection begin only after they have logged off. 

I appreciate the quick response and suggestions regardless!