Is it possible to model a PIN InGasAS photodiode in a SPICE simulator?
Yes, you can model a photodiode with a circuit in SPICE. And the circuit you linked will work.(figure 3 of : http://www.osioptoelectronics.com/application-notes/an-photodiode-parameters-characteristics.pdf)
But first, I suggest that you read that entire document to really understand what a photodiode does and how it works.
You don't seem to get that :

Photodiodes operate by absorption
of photons or charged particles and generate a flow of current in an
external circuit, proportional to the incident power.

And this is in the first paragraph of the document you linked.
See also :

https://en.wikipedia.org/wiki/Photodiode where they have another equivalent circuit (easier to understand but far less detail)
a very similar question : Calculating photodiode current based on A/W for simulation
another one : Equivalent circuit of a photodiode