The heat of the volcano wouldn't change anything. The problem is first that you can't guarantee it won't be carried on magma currents and be pushed above ground

The heat of the volcano wouldn't change anything. The problem is first that you can't guarantee it won't be carried on magma currents and be pushed above ground elsewhere, and second if it got stuck and didn't sink into Earth's core, you'd have a volcano dirty bomb just waiting for the next eruption. And you'd have no way of knowing if it got stuck or not.