Some of you are absolute dolts. In what world do you think a coach can just jump in a dual meet race and cruise around the track with their athletes? If this poster didn't seem so sincere, I would think they are trolling.
A high school coach is no longer a high school student, and given that this was a high school only race(unless it was an intra-squad meet), they are not allowed to just jump in and pace, compete, or participate in anyway. Their place is on the sideline.
We aren't talking about an open USATF race, or a Pro-Level race. This is your standard weekday affair that most teams use as a workout.
The only time I have ever seen this is when there are Unified Athletes(Special Education Students) who need an adult to participate with them, and even then, if they can get a student to do it with them, they will.
So, No, if your state uses NHSF rules, a coach may not compete in a high school only sanctioned event, IN ANY SPORT!