It's an interesting idea but Fedex isn't going to sideline a few packages for someone to come pickup later to deliver. They try to work in bulk as much as possible, otherwise the cost per package increases too much with one-offs. And what would be the benefit to them? Highly unlikely it would be cheaper for them to have you deliver it at $10-$20 than their regular driver who was near that neighborhood anyway.

Amazon is kind of already doing this with their flex driver program. They'll deliver a few dozen packages though on a 3-6 hour route. Any volume less than that makes the whole thing too expensive for them.