Actually, no. The Apple AirTag relies on two things to be able for you to see its "location" on the Find My app on your iPhone: 1) Bluetooth, & 2) The Apple's Find My Network (which literally consists of millions of iPhones)
The key is that an iPhone, with an active Internet connection, must be within an unobstructed Bluetooth range (~30-40') to pick up the tag's Bluetooth signal. That signal is transmitted approximately once every 3-5 mins. to save battery life. With everything in place, the phone will relay the tag's ID, & the phone's GPS location over the Internet to the Apple servers. That is where you would see the updates on your phone.
As you can see, a number of things would have to happen for this to work smoothly. So, for example, if you place the tag inside your luggage, and you happen to have a hardened (think metal) suitcase, then the tag's signal may not be able to transmit thru. Another would be, if no iPhone was nearby within a transmission, it wouldn't "see" the tag, let alone relay its info to Apple.
What would be surprising would be if the tag is at a busy airport, or any "busy" location, where there are many iPhones present, that at least one of them would not be able to "see" the tag ... unless that tag's battery was depleted or that it is defective.