If they have a slow reaction time, they wouldn't be on time stopping it either. Their reaction time applies to both events.
If they are consistant on the time it takes to hit the button after it crosses a line, then the calcs will be accurate. The more consistent your timer is, the more accurate the calcs.

It doesn't really matter if the timers reaction time is slow, as long as it is consistant.

Discussion of reaction time is pretty much moot anyway since the timer can anticipate it crossing the line. It's not like you have to respond to a sudden event like a light coming on. You can see the truck approaching, then crossing the line. Hitting the stopwatch button as it crosses should be pretty simple to do consistantly. The timer should also be able to tell you if he got it right, or missed by a bit and should discard the run time.

As long as the lines are accurately measured, and the guy with the stopwatch has a clear view of both lines, you should get numbers as accurate as any radar. Probably better.