What can be inferred from the frequency an op-amp is oscillating at?
The terminology is a bit confusing - but you must distinguish between "open-loop gain Aol" (gain of the opamp without feedback factor B) and "loop gain (Aol*B)" (gain of the complete loop).
Thus, if an opamp with feedback oscillates, you can assume that at the oscillating frequency the loop gain (AolB) is unity. More than that, it is correct that at this frequency the loop gain magnitude roll-off will be app. -40dB/dec (phase shift -180 deg). However, at which point of such an asymptotic line you will find the pole frequency?
This is possible only if you know the first (lowest) pole frequency      

Therefore, the best method for identifying the second pole is to record the magnitude function vs. frequency.