Yeah the rain will act to strengthen an already existing inversion. Obviously with convection you can get some stronger downdrafts that can mix down to the sfc. My strongest downsloping is usually with abundant virga and very light precip reaching the ground. That evaporative cooling can give the downdrafts a little extra boost. Overall the higher and more mixed the layer is from the sfc the better off you’ll be. The coast this time of year gets good mixing in these systems with flow off of the warmer waters.