Don't think distance matters, even though they don't see a GPS chip. Read this snippet from an AirTag article -
Quote
So, how does Apple allow users to find lost items using the AirTag tracker? Unlike iPhones, AirTags do not come with an in-built GPS chip. In place of a regular GPS chip, the U1 chip is adopted. The tracker relies on this innovative chip with ultrawide-band capabilities that creates a network of 1.65 billion individual apple devices to locate any particular item. This means that the tracker can surpass the limitations of Bluetooth and Wi-Fi connectivity for effective tracking.
I recently forgot to keep my pickup key AirTag when I dropped it off to be repaired.... drove me nuts - constant updates about it's location, even when they test drove it.