Relation for the current generated by a photo-diode in photo-conductive mode
As a first-order approximation, the reverse bias and loading resistor don't affect the photocurrent at all, so you have the correct formula:

$$I_p = P_o {\mathcal R}$$

In reality, these will have a small effect, but to account for it, you have to know the diode's effective shunt conductance. Then you can model the photodiode as a current source in parallel with the shunt conductance (and some capacitance if you want a dynamic model).

You may be able to estimate the shunt conductance from the photo-current and open-circuit voltage curves given in your device's datasheet. At 100 uW/cm2 (1 W/m2), I'm estimating about 32 uS conductance, or 30 kohms resistance. The conductance increases as optical intensity increases.