Prior to observation, the electron can be found anywhere (from inside the nucleus to the ends of the universe), but once its position is determined the answer is precise (albeit its momentum is not due to the uncertainty principle).
I have several questions related to this idea
First, how do you actually determine the position of the electron without "kicking" it out of the atom?
Second, if you were able to determine its position very precisely, wouldn't its momentum be so high that it would exceed the speed of light? (or does it just become more massive? Either way, it doesn't seem like it could remain bound to the nucleus.
Third, if you were able to determine its position, how does your knowledge of its position degrade with time? It would appear that to get back to its original probability distribution (over all space) it would need a great deal of time, again so as not to violate the speed of light (unless it can pop in and out of existence far, far away).