For a plane with a pusher propeller, how does a root-stalled wing affect its performance?
Interesting question. Its far easier to find studies which focus on effect of propeller on the wind aerodynamics. I highly doubt there would be any analytical equation that can give effect of stalled wing on a pusher prop. For one thing, stalled airflow goes out of the realm of what analytical aerodynamics can handle. Even for having an empirical equation, since the stall is highly irregular phenomenon, it would be very difficult to arrive at any empirical equation which can give reasonable correlation for wide enough envelop of wing-pusher configuration. The impact would be highly sensitive to geometric configuration parameters such as location of propeller with respect to centreline, distance from trailing edge and so on. For a specific configuration, one perhaps could come up with a correlation but that would need a good amount of experimental data and it would be of limited utility.

In my opinion, the impact of the stalled wing on the propeller performance is far less than the impact of the propeller on the wing stall. Definitely there would be some impact on the performance on the propeller due to "dirty" incoming airflow on the pusher propeller, but the impact should be small. I base my expectation on the fact that the streamwise velocity would be still much higher than the cross-stream velocity components in the stalled airflow behind the wing, thus giving marginal changes in AoA that the propeller blade aerofoils see. This particular research paper say this in the conclusion:


  The prop-wash effect mainly increased the aerodynamic performance of the wing, but the wing–wash effect was just a small part of this interaction. However, the wing-wash effect cannot be ignored as also mentioned in previous study.


Note that this is valid only for lower Re regime for the particular configuration studies. But I would expect results not too different in other cases.