Why is the 1 mH (inductor) in this design? What happens if I probe at 23/54 to measure CURRENT without having the 1mH?
If you measure current by shunting yoke, then you short out the current supplied by R90 (0.249Ω). n.g. so just keep yoke connected and sense current on pin 50 via R101.

To operate without an Hcoil may not damage these parts, but it won't work as required. Beware of HV Flyback transformer for Hsweep.

The circuit is designed to deliver a controlled current sawtooth ramp to drive the yoke with a linear sweep.  The amount of current is determined by the yoke defection power coefficient given in mH*A^2 for peak current which is also dependent on coil inductance.   

Normally the ramp of current is sensed and compared outside this cct. to correct the linearity of an integrated pulse current in a polystyrene cap normally. This is not the complete circuit.