Ok so I ran some quick tests, and here are my results. Firstly I will describe how I measured the results of the sharpening applied, I did this by simply loading all of the exported files as layers in PS and setting the blend mode to difference. This then gives you a bitmap that shows the difference between each pair of layers a a colour. The brighter the colour the bigger the difference. Since we are actually dealing with very small values most of the time I also added a levels layer at the top of the stack just to brighten the result so that you can easily see what is going on. I added a 10 sampler points, which with the levels layer active lists both the actual pixel value, and the value after adjustment.
So with a method for analysing the results I ran the following exports from LR, and to be sure that there was no variation between instances I ran each export twice. I did my first export with no sharpening, so that I had a base to work from. I then exported with the resolution set to 100 PPI and 200 PPI and also ran Screen Low and Screen High as the sharpening. After assessing these I went back and added 72 and 300 PPI but only at Screen Low. There was zero difference between any of the pairs as you would expect, and contrary to the belief of some (including me) there was zero difference between any pixels when changing the resolution value. There was though measurable but small differences between high and low levels of sharpening. Compared with no sharpening Low gave the following stats, Mean: 0.93 SD 1.28, Median: 1 and I think maximum value was 29. None to High gave 1.66/2.22/1/51.
So I then repeated the test for printing, and I selected Glossy paper and again went with Low and High settings, although I only ran one export of each case, using the following PPI values: 72, 100, 149, 151, 240, 300. I later added 400, 600 and 1200 PPI. The results for this test were rather more interesting, with changes to the resolution having a significant effect on the sharpening. All of the output resolutions from 72 to 151 PPI all had exactly identical levels of sharpening. There were measurable differences between those and the next value, 240 PPI, and then also between 300, 400 and 600 PPI with each resolution getting a different level of sharpening. There was zero difference between 600 and 1200 PPI. So for the paper options there seems to be a band of values that result in sliding levels of sharpening.
Something that I hadn't considered was that the sharpening level went down as the resolution increased, for some unknown reason I had expected it to be the other way around, although at either level or any resolution the print sharpening was much higher than that for screen. That is assuming that the larger the difference between pixel values implies more sharpening, since it is a bigger change. I have saved the PSD files, so if anyone is interested in seeing the results ask and I'll put them up on Dropbox.