Is it possible to evaluate the exact diagonal length of a square using Pythagoras theorem?

That depends how exactly the measurements of the sides are - and how exactly the "right angle" is really a right angle. If the measurements are exact, then, yes, you can also calculate the diagonal exactly - using Pythagoras' Theorem.

.................................................................................................................................

Improved Answer:

No it's not possible to find the accurate length of the diagonal of any square using Pythagoras' theorem because the answer will always be an irrational number which can never be determined just like the value of pi in a circle.