It will actually fit in the phone, just stick out because it's not the same length. That being said, Air Command does not 'reside' in the S-Pen. Yes, the hardware is compatible with Wacom's system (you can even use the S-Pen on a MS Surface and viceversa!), but the Air Command feature is purely software.
So yes, it's possible to implement on the Note 3, and I'm sure someone out there has done so. I'm not too savvy on these hacking matters, but you'd need to root your phone and install a new ROM with that feature 'baked in'. There might be 3rd party apps that emulate this function (but don't really know if any exist though) and although I can't see why, they may or may not need root to work (in the end it's just a mini-launcher for your S-Pen).