During a measurement ride with my son today I got a flat rear tire at just before the 4-mile mark of our 8+ mile measurement. We were scheduled to go through the Detroit/Windsor Tunnel at a scheduled time when they planned to shut the whole thing down for us. Since we didn't want to miss that time I decided to continue the measurement with the totally flat rear tire. I was a little concerned about how it might affect the measurement, but decided to chance it.
After the measurement we looked at the numbers. For the first 4 miles with my intact rear tire, our measurements differed by 1.8 meters. For the next 4 miles with my rear tire flat, our measurements differed by 2.0 meters. Both times my son was shorter.
Before this unplanned experiment I would have thought that a flat rear tire might change the way you ride enough to affect measurement numbers. But at least in this case any such effect was trivial.