Bluetooth 101 - novice question

Not an engineer. Just someone trying to investigate a product idea. Have technical questions, eager to learn. If you can take a moment to point the way, I'd appreciate it immensely.

Suppose I use an app on my smart phone to set an alarm on a paired, bluetooth-enabled alarm clock. The alarm is set on the clock. The pairing is later interrupted. Does that affect the alarm set on the clock? Or can a timing component and micro controller run the alarm program without continuous, uninterrupted pairing to my phone?

Interrupting the pairing shouldn't affect the alarm at all unless it's a very badly designed alarm.

Mike.