I don't think it would work. I think that the reason nothing grows in the school yards is that with the kids playing on it all the plants/weeds get trampled.

For whatever reason it seems like weeds thrive in compacted areas. Maybe it's because they don't have competion from other plants.

Here are the options are I can think of to prevent plants from growing in that area.

1. Put down a layer of landscape fabric and cover with rock or wood chips.

2. Spray with a long lasting herbicide. You will need to do this on a regular basis. This might be a bad idea as it could cause erosion.

3. You could put a layer of concrete or asphalt down and paint it green that way it would look just like grass.

Thanks rgress, I will mostly go for option #1. Dont want to use any chemicals and want to keep the option of growing something there at a later time.
Is it necessary to put down the layer of landscape fabric? Can I just cover it with wood chips?

thanks again.

As long as there is moisture, and even a little bit
of light, and a growing medium, (even clay), then
a plant seed will sprout, eventually. Whether it's
a weed, or not, depends entirely on what your definition
of a weed is.