OP-AMP Output Voltage
Yes, the output voltage of your amplifier is independent of the power supply voltage, as long as that power voltage is large enough.  Of course it can't be so large as to blow up the opamp either.

Note that the direction of the photocell current of the diode is down in this instance.  That means the current flows right to left thru the resistor, and the right end of the resistor will therefore be at higher voltage than the left end.  Due to the closed loop feedback, the opamp will make its output whatever it takes so that its negative input matches its positive input, which is ground.  The output will therefore swing from ground (0 V) at no light to some maximum a full light.  The power supply range must include that, plus whatever headroom the opamp needs to operate correctly.

If this is a "rail to rail" input and output opamp, then the negative output of the supply can be connected to ground, and the positive needs to be at least whatever the maximum output voltage will be due to the brightest light.