It depends.
If && is the usual short-circuiting logical operator, then it's fine because there's a sequence point. array[x] will use the new value.
If && is a user (or library) defined overloaded operator, then there is no short-circuit, and also no guarantee of a sequence point between the evaluation of x-- and the evaluation of array[x]. This looks unlikely given your code, but without context it is not possible to say for sure. I think it's possible, with careful definition of array, to arrange it that way.
This is why it's almost always a bad idea to overload operator&&.
By the way, if ((x > 0) && array[--x]) has a very similar effect (again, assuming no operator overloading shenanigans), and in my opinion is clearer. The difference is whether or not x gets decremented past 0, which you may or may not be relying on.