what do you mean by "energy is greater than the potential of the well"? Do you mean E=K+V>V? But that's always true. Or do you mean total energy is higher than the height of the well, e.g. E=K+V>|V|, in this case since E>0 it's not a bound state let alone ground state.
And I think the uncertainty principle is not a very good way to analyze finite square well, because the particle is not strictly confined inside the well, you can't know for sure the narrower the well is, the smaller delta x is (I don't know if this is true in finite square well case, but anyway you shouldn't simply conclude that without calculation). But I think probably it's ok (but still not rigourously correct) to use it analyze infinite square well,because the particle is not allowed to go outside.
