No, generally it is not. It could be zero for specific loading conditions. Since they are equal but with opposite signs then their average is zero.
For example, if you put a stress element under tension in the x direction and compress it in the y direction with equal stresses such as sigma_x=sigma_y, this will give you a stress element if rotated by 45 degrees will give you the maximum shear planes with zero normal stresses. So generally that's not the case. The general case is that you will get the average normal stress when you get the maximum shear stress. In the example I mentioned before if we consider the compression and tension natures of the stresses, we assumed then sigma_y should be negative because it's compression and sigma_x is positive because it's tension.
Learn more about stresses here-
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