Since you are using a shallow dug well for the drainage, and you are not using the water for drinking, I don't see how that is a problem. In some ways this is like using the dug well as a cistern.
The dug well is using surface water filtered through the upper soil. Rain water that falls on the soil surface is likely in your well the same day. All you are doing is moving surface water around.
You would never want to direct drainage water into a drilled deep well, though. You might pollute the local aquifer and even if you aren't using the well for drinking, your neighbors might be using the aquifer for drinking.
Our area has numerous springs. Last year I put in french drains under my barn thinking that it was always wet due to lack of drainage of rainwater. At the same time I dug a 4 foot trench for a livestock waterer running from under the barn out into the neighboring field.
When digging the trench, it filled up with a foot of water overnight. It turns out that there was a small spring under the barn. I ended the trench with a french drain out into the field because standing water is bad for the livestock water system. I "daylighted" the pipe on a downslope so that I'd have access in case it needed to be snaked in the future. Now I have a dry barn basement and a continuous spring fed puddle in the field that stays liquid even in the winter.
The funny things is that the cows prefer to drink from the puddle all winter rather than the waterer.
