App - will staying connected drain my battery

If my app stays connected to a device when the device is not on, or in BT range, will this drain my phone’s battery?
Will my phone actively work to find the device?
Or will it work like any other BT devices, that you are pairded with, but no disadvantage to just stay paired untill it is powered on/in range?
When I do this I have a constant notification on my phone that Meshtastic is disconnected.

My base question is, should I choose to disconnect in the app’s settings when I am not using the device?