You don't actually "push" the film until it is developed. When you shoot it you are just underexposing it. That said, if the film is pushed in processing it will cause any effects of any x-rays it was exposed to to be pushed as well.

As far as to whether it is even worth trying to get such a roll hand inspected: it probably is since the worst that will likely happen is they say "No" and run it through the x-ray anyway. You might make some small, simple paper labels you could attach to the film saying "expose/process @ ISO1000". This would lend credence to your plans to push the processing.

Whether there would be any actual benefit from not running it through the x-ray could best be answered by shooting an experimental roll, running it through an airport x-ray, and then pushing it in processing to see if the x-rays leave any artifacts. But even then the amount of exposure from one x-ray to the next could vary based on the settings of the machine and how fast the conveyor moves the film through.