The Scotlandish app on iPhone can have checking effectively disabled* by you turning off the phone, turning off the checking, or turning off Bluetooth. So it doesn't quietly turn Bluetooth on, no. That would be prompted -various apps generate a prompt to open Settings if they want me to tun something on for them.
* This might be in the article about this one... it's if you work with the public through a perspex screen so not at risk, if your phone is not actually with you e.g. you leave it in a locker at work or at the gym, and I think there was something else... which wasn't "If you are outside Scotland and you should be running a different local contact app instead". Unless it was.