Looks like that’s an ineffective approach.

I commented elsewhere with an explanation and a bit of speculation. I did later confirm that even ‘disabling’ Bluetooth doesn’t stop the attack.

The attack method works even when Bluetooth has been disabled using airplane mode from the control panel, which may surprise you. In which case, you’ll be shocked to discover that disabling Bluetooth this way, erm, doesn’t. Instead, you’d need to disable it directly from your device settings or run your iPhone in Lockdown Mode to prevent these advertising pop-ups from being received.
Source

Assuming similar on Android, it’s possible, but not that easy toggle everyone knows about.