Mike Sandford, who did a lot of testing of calibration rides with different tires and different road surfaces, said that he believes the calibration differences due to ambient temperature changes is due more to changes in the tire rubber properties than to changes in the tire pressure.
Based on anecdotal experiences I tend to agree. Early on in my measuring career when I used a wider "beefier" tire I would see big changes in my cal constant when the temperature went up. After I switched to a high pressure, much thinner tire, I did not see as much cal constant change with temperature change.
Also, the theory behind the "effective radius" says that it is dependent on the tire pressure, but it is also very dependent on the friction coefficient between the tire and the road surface. Taken to the extreme, if that friction coefficient is zero, then there will be no change to the "effective radius" of the tire even as it flattens more or less against the road surface due to changes in tire pressure.