I've seen people over the internet aiming their flashes to the umbrella's axis but haven't seen yet a before and after photo. In my case, the flash aims a bit above the axis. What would be the benefit of aiming the flash to the umbrella's axis?
The benefit should be a bit better effectiveness of the umbrella and less spill outside. If your flash isn't significantly off I doubt that the change will be noticable.
Asymmetric lighting of umbrella may also show up as asymmetric catchlights in subjects' eyes.