The cue ball only knows where it got struck, and how hard. It doesn't care what your hand 4 feet away is doing 
However when you clench you bring in extra muscles, and these muscles might alter where the stick points or how the arm swings (for example, causing the butt of the cue to move outward, which means the point of the cue moves inward, which would affect where the tip hits the ball).
Generally if you don't need to use extra muscles, you should avoid using them because it just complicates the stroke. And you definitely don't need them to get good action on the cue ball.

However when you clench you bring in extra muscles, and these muscles might alter where the stick points or how the arm swings (for example, causing the butt of the cue to move outward, which means the point of the cue moves inward, which would affect where the tip hits the ball).
Generally if you don't need to use extra muscles, you should avoid using them because it just complicates the stroke. And you definitely don't need them to get good action on the cue ball.