Yes, GPS can often still work on an Android phone while airplane mode is enabled. The important distinction is that receiving navigation-satellite signals is different from transmitting your location over mobile data or Wi-Fi. Your phone may know where it is while nobody else can see a fresh location online.
Airplane mode primarily exists to disable radios that transmit, especially the cellular connection. Modern Android phones may let you turn Wi-Fi or Bluetooth back on while airplane mode remains enabled. GPS/GNSS is different: the receiver mainly listens to signals transmitted by navigation satellites, so it does not need to send a radio signal back to those satellites.
That is why many Android devices can continue calculating a satellite position in airplane mode. Device software and settings differ, however, so test the exact handset you intend to use rather than treating one phone's behavior as a guarantee for every model.
A local position and a remotely visible position are separate things. LocationOf or another GPS logger may be able to obtain or record coordinates while the phone is offline, but an online map cannot receive those coordinates until the phone has a working internet path.
If airplane mode disables both mobile data and Wi-Fi, the newest server-side point can therefore become stale even though the handset continues to receive GNSS. Once connectivity returns, an app designed for offline recording may be able to upload stored points with their original timestamps.
It can. Phones use assisted location information, network time, Wi-Fi observations and other data to make positioning faster and more robust. With all networking disabled, the receiver may have to obtain more information directly from satellites. A first fix after a long period, a large journey, or a device restart can therefore take longer.
Go outdoors with a broad view of the sky and give the receiver time to settle before deciding that GPS has failed. Inside a building or between tall structures, poor satellite geometry can matter more than airplane mode itself.
An offline navigation app can still show your position if it already has the required map data stored on the phone. If the map itself must be downloaded from the internet, you may see a blank or incomplete map even though a valid coordinate is available.
Think of the process as three layers: positioning tells the phone where it is, map data draws the surroundings, and connectivity sends information to other people or services. Airplane mode can affect the second and third layers without necessarily disabling the first.
Do not perform the experiment in a situation where you need mobile connectivity for safety or emergency communication.
LocationOf should be treated as two functions working together: the Android device records location, and the internet connection transfers records to the website. Airplane mode may interrupt the second function. It cannot give the website a magical communications channel to an offline handset.
For the broader explanation, read Does GPS work without internet?. If you are considering a dedicated phone without cellular service, see Does GPS work without a SIM card?.
Airplane mode should not be used as a substitute for Android permission controls. If your goal is to prevent an application from receiving location, review that application's location permission and the device-wide Location setting. Airplane mode mainly changes radio connectivity and can be configured differently on modern devices.
Likewise, an old point already stored on a server does not disappear when airplane mode is enabled. Always look at its timestamp. A map that still shows your previous position may simply be displaying history while the phone is offline.