Can I leave the air conditioner on with the doors and windows open?

Sure, but why would you do this when your question obviously denotes you know you shouldn't. 

Sure you can, but it would be dan stupid to do so. It will over tax the unit and could cause it to burn out!   Not a brite move on your part! NOT AT ALL BRITE MOVE!

could cause global cooling

Yes if you want to waste energy cooling the universe.

No, I can not leave the air conditioner on with the doors and windows open.

why , use your brain if you have one .

yes.  But you will burn out the unit.  It would run constantly.

To what purpose ??   But . . .  when I was a kid my mom had one of those Lincoln 4 door convertibles and it had air conditioning.  We thought we were big shots driving around with the top down, windows-up with the AC blowing cold air on our faces.  But we were just stupid fools.

I assume your vehicle is stopped while you do this correct?  

You can but it won't do a lot of good unless your face is right up to the vent. If  you have a reason to do this, I would pop the hood and leave it up a little bit to help keep the engine from overheating.

just try it and see and then you'll know