As a former track and cross country coach in Ohio I think I can answer this one. While the OHSAA will allow you, since coaching officially begins on the 10th, I highly doubt your coach would want you running a road race during training. So in this instance it would be best to check with the coach and not the park.
2009 OHSAA Cross Country Calendar
Aug. 10 First Day of Coaching
Aug. 24 Season Begins
Sept. 21 Non-Interscholastic Competition No Longer Permitted
Oct. 11 District Tournament Draw
Oct. 24 District Tournament
Oct. 31 Regional Tournament
Nov. 7 State Tournament
Nov. 7 Season Ends
5.3) Road racing is interpreted as a different sport than cross country. If the entire race
is run on a road, participation is not a violation of the non-interscholastic competition
bylaw.