from a purely physiological point of view, yes, it would be feasible, since a 5k race serves as a good VO2 max workout, and you can get by with only one VO2 max workout a week.
HOWEVER!
Remember that you are coaching people, not robots! If your runners haven't done ANY 5k paced workouts going into a meet, they will be very nervous. Most high school programs do at least one workout at 5k pace per week. Some do 2 workouts at 5k pace, but if done several weeks in a row, might be risking overtraining some athletes. If you raced every saturday, you could do a 5k paced workout monday, and a "lighter" (i.e. different paced) workout wednesday--maybe cruise intervals and some fast 200s late in the season, or a tempo run (T pace or M pace, your call) or hill workout early in the season.
Don't worry TOO much about overkill. Even if you did two VO2max workouts every week AND a race every saturday, that's less than many high schools do. Some coaches (albeit not the good ones!) have been known to do monday workouts, tuesday dual meets, thursday workouts, and saturday invitationals.