op amp rails and its inputs
The voltages will likely go beyond +/-0.7v in practice. The 1N4007G datasheet specifies Vf or the maximum forward diode voltage at about 1.0v when 1A is passing through it. It can take more current than this, up to 30A, for a very brief period of time however. If L1 is a high-power device, more than 1A could flow through either diode briefly, pushing the measured voltage higher than 1V, likely up to +/-3v. Test it and record the output using an oscilloscope for real-world values in your circuit.

Note that the 1N400x series are relatively slow and are optimized for rectification purposes. The collapsing magnetic field in L1 when the key is released, will ramp up voltage very quickly. A faster diode may be needed to prevent large voltage spikes from forming. Again, test it and see.

Anyways, a comparator outputs it's positive rail voltage when it's positive input is greater than it's negative input. It outputs its negative rail voltage when the positive input is less than it's negative input. 

In general, you can't drive an op-amp's inputs beyond it's supply rails. So it is not possible to power the comparator from 5v and 0v, then apply -3v to an input. How this is mitigated is by the use of resistor dividers to "scale" and align input signals to values falling within the acceptable range of the comparator. Same with it's output.