We should probably make a thread on this on the general board but I'll give you one example wich is a little extreame but is proof pudding!

I was doing a couple of photo runs in my Bullet and running against a 2mph current. My gps read 83.6 mph but my actual speed over water was 85.6 mph. Had I been going downstream with the current my gps would have read 87.6 mph but I would still only be going 85.6 mph over water. The gps speed is speed over ground and had there been no current at all the gps would have shown 85.6 mph because speed over ground and over water would be the same. Most boating isn't done in such currents but the gps cannot compensate for any current or cross currents (lakes and waves) and the differences are enough to effect test results. A pitot system would have shown no changes in speed whether going up current or down current. Or across current.

You are correct that different props will affect the pitot reading but not as much as you are thinking. If the pitot is in clean water (from the boat bottom) and is set up correctly it will not show much change due to different transom angles. Water density can play a role in pitot accuaracy but you are testing in the same density so your results are still reliable.