Will this servo stall detection circuit damage an Arduino?
No, you are not likely to damage your Arduino with this setup. In fact, the diode is probably unnecessary, because the R-C filter severely limits any transients to begin with. The resistor alone limits the current through the pin to no more than 1 mA for any sustained voltage in the range of &plusmn;75&nbsp;V.

The bigger problem is that this whole scheme relies on the fact that the V1 source has some definite value of source impedance, and you're measuring the voltage drop across this impedance in order to infer the current being drawn by the servo. If you were to change to a different source (higher current capacity, lower source impedance), the whole thing could stop working.

That's why most published schemes use an explicit current-sensing resistor &mdash; to remove that dependency and insure that the circuit works with any source. If you're really concerned about the power lost across such a resistor, you could use a Hall-effect current sensor instead. There are several commercial devices available for this.