I recently purchased a self-rimming sink without an overflow. I have two small children at home. Was this a mistake? Should I return the sink in case they decide to turn the water on and leave it running or does it really matter?

Assuming you are referring to a bath lavatory sink. If you have not installed I would return it. Most lavatories have an overflow. I have one that does not. Didn't notice until after I had installed it, but I have not small childern.

I am referring to a bath lavatory, and no I have not yet installed it. The only problem is that the toilet and tub are Kohler and I do not see that they make a self-rimming sink in the size I need with an overflow. I did not know if the overflow actually made that big of a difference.

Have you check to see if other sinks by Kohler of that design have an overflow. Maybe a worker just forgot to put in the tubing to make the overflow. I visited the Kohler factory once, its still largely a manual process. Didn't see a single job there that I wanted. They still build a sand mold in a box, punch out the holes, fill the mold with the proper stuff and fire it in a kiln. The overflow doesn't matter if you never forget to turn the water off. So far I haven't.

Just fit it with an electronic faucet, but then a cup of water to drink might prove difficult.