Try it and you'll see. Battery optimization on radios is WAY better than it used to be, so even the BT radio being on all the time won't make that much difference in real-life use (again, unless you're ACTIVELY using it). The window shows up every time you turn BT on to select devices around you, but yeah, any auto-enabled connections will happen with or without that window, which is why if you keep BT on in your phone, it will automatically connect without the window pop up when you turn on your car and are within range or when you turn on your headphones.
The volume warning, yeah, I agree, is annoying, but a valid warning nonetheless. That being said, you only receive it once per reboot. If you don't reboot your phone, the pop up gets dismissed once and it doesn't come back until your next cycling.