Sticking an aquarium air pump inside my pot
 

What could go wrong?

I'm not sure I understand what you want to do. Can you explain a bit better, and what your goal is by doing that?

Worst case scenario, you're electrocuted and your house burns down.

Do you want to create air movement inside the pot?
To that extreme a basket is better.

oxygen to the roots

To which orchids do you want to apply that solution.
The best to achieve that is a basket with a coarse medium.

Do you mean putting an airstone in the pot? As rbarata suggested a basket is the most commonly used method of providing air to the roots. You'll complicate things such as watering and emptying the pot, plus you'll have the sound of an aquarium pump running.

I have never seen it done, that's not to say it won't work, but there are tried and tested ways out there which are a bit simpler - and effective.

If this is for your Phal. It's not necessary.

I agree with this. A pot with sufficient drainage holes and even ventiliation slits, combined with a coarser media will provide all the air flow that the roots need.

And a constant air flow through the medium will dry it too fast...maybe faster than a mount.