I think radius can have an affect, but I'm not sure if it's enough to be significant.
Think of a 5 string bass, as it has a string in the middle making this easier to visualise. The string in the middle is parallel with the neck, but due to the nut width being narrower than the neck pocket, the other strings fan out slightly. For any string at an angle like this, on a flat board, everything is constant, just like the string that goes straight down the middle. But on a radiused board, the frets get further from the string the higher you go due to the curvature.
Take it to extremes and picture a baseball bat with 3 strings anchored to the same point at the 'nut' but widely spaced at the 'bridge' and you can see that on a bass this must have a similar effect no matter how subtle.