A Sink Overflow Hole does more than you think.
The little hole that you see in a lot of sinks that many refer to as a sink overflow hole, actually is there for a different purpose that the name indicates. Sure, it can help when you have your plunger down and forget to turn off the water. But, it probably will not let enough water drain out to stop your sink from overflowing. It is just not a large enough hole to do that.
The main purpose of the sink overflow hole is to allow air into the main drain at the bottom of your sink so it will drain faster. The movement of the air into and out of the drain forces the water to flow out the drain pipe much easier.
Sinks that are designed with some type of overflow holes are usually more efficient than sinks that do not have some type of drain vent. To help ensure that your sink drains properly it is important to check the overflow hole on occasion to make sure that it is clear and clean. Any type of build up in the hole may prevent the air and water from not flowing through the vent and your sink will drain out much slower.
On occasion just run a small wire or plastic tie into the hole to make sure it is clear. Keep the hole clean and you will be rewarded with a sink that will drain the way it is suppose to.