Can a paired/bonded bluetooth device wake an Oreo or higher Android device

Question

I have a security system where moving a Bluetooth LE device causes my android application to do some work. After some of the newer Android updates, I believe API 26, I could no longer get these updates if the Android device's screen was off. I was trying to think of a way around this and came up with an idea:

What if I paired the Android device and the Bluetooth device - would this allow for the message to be received when the Android screen is off?

Previously, all my BLE devices were part of a mesh, so I would regularly have the Android app check for changes in the mesh and turn the screen on to notify the user if needed. Now, because of the background execution limits introduced, I must require the Android device to have the screen on at all times, which leads to the death of display over time.

I'm not that great at programming in C, which is the language the BLE chips are programmed in, so I wanted to ask this first before spending hours just to see this NOT work. So, just to repeat the question: Will having a BLE device paired with the Android device allow a message through these restrictions when the Android screen is off?

If not - is there a way I can make this work?

Thank you for any info!