No way! You finished your job before scheduled time and you're not informing your manager? That's totally irresponsible! There could be another task on project's critical path that's waiting for you!
So... what I want to half-jokingly say here is: don't wait until last moment. Double and triple check if your job fulfills the requirements, but do not extend the scope on your own.
And remember
“Perfection is achieved perfection not when there is nothing left to add, but when there is nothing left to take away” – Antoine de Saint-Exupery