You'd get the same result whether you test the hypothesis y > x (with both random variables) or y > 0. Under the null, the p-value is uniform on [0, 1], whateve

You'd get the same result whether you test the hypothesis y > x (with both random variables) or y > 0. Under the null, the p-value is uniform on [0, 1], whatever that null is. It follows from the definition of a p value. (Disclaimer: I am not a real statistician....)