That would work as long as it doesn't fill up too quickly. Looks like a neat solution. Water over a dirt road never works out. Also water speed is a factor. Too slow and silt builds up, too fast and you get erosion. I have seen builders use silt fencing, rocks and straw bales to slow the water down enough to drop the larger solids in a hole they dug, similar to the precast pit you found, but might be easier to dig out.
In my case I have given the drain a bit more fall so hopefully there will be just enough speed to flush out the leaves and silt in the bigger flows to keep it clear for longer. Time will tell.