There can be a significant difference between a simple coil, and a transformer. More information would help, where is the device being used, how about a photo? If what you are dealing with is not potted or sealed, so that you have access to the winding's, it would be possible without destroying it. Cheers, Richard
If it is an open-frame EI transformer, it is often possible to thread a few turns of insulated wire through the core over the existing coil. You can then make a fairly accurate determination of actual turns by exciting any one of the windings with a few volts from a signal generator or Variac, then comparing the ratios of measured voltages of the unknown windings with the voltage across the known turns count of the added winding. When the core is not accessible, measurements of turns ratio and core saturation point will get you close. An accurate DC resistance measurement of the windings will determine the wire gauges used.