air data reference measures the aircraft's position
No.Air Data is AIR data from your pitotS and static portS.
Aircraft position is calculated via Inertial Reference UnitS among others such as GPS.
To answer your question,if for example the air data computer of Captain gets info different from the ADC of the FO,the crews will be alerted as for example speed disagree as mentionned above.
The 737 has two AIr data computers linked to two Inertial reference units called ADIRUs.