Does Arduino Mega 2560 R3 have schmitt trigger in GPIOs ?

You confuse hysteresis with a gray area.

The pin will certainly be HIGH above 3 Volt.

I know what you mean, but if OP doesn't solve those low logic levels, then it's pointless talking about hysteresis.
An analogue input could solve both problems.
Leo..

It's a digital signal from our RF switch module. We have to control servo motor which is the brake of our EV car with our RF switch. When the voltage rises from 0 to 5V we are afraid the servo works randomly during the grey area

If it is a normal digital signal then it will pass through the "gray area" very fast and it should not be a concern.

How long does it stay in this gray area?

What is this RF switch?

We are afraid of signal being chattered between 1.x ~ 2.x V

How do you know this? Did you measure it with a scope?