Can I use a clamp meter to identify wires running to overhead fan?
If by "clamp meter" you mean a non-contact AC Ammeter, and if the circuit can be loaded enough to trigger the reading.  Yes, you should be able to isolate the circuit using such a meter.  (Keep in mind that this type of meter only registers AC current so you must have current flowing for it to read.)

On a related note, however, that box looks to be severely overloaded.  You may want to consider upgrading it as this may be unsafe.