Is the small hole beneath shower diverter valve for preventing water overflow when a person makes the tub full of water, for taking bath?

Hi Yousuf:

Yup! If I understand your question... this overflow hole is exactly as you thought... see picture below. Here is what it looks like behind the tub.

If tub overfills then water should run down this overflow hole to help prevent overflow of the tub. It will not reduce risk of overflow for too long though if say tub is running and knowone is present. In this case, tub will eventually overflow the overflow hole and finally the tub.

Let me know if need more on this...

MARK

It also helps serve as a vent for you tub drain. It allow air into the drain so the trap will not siphon out its water.