That's correct. As with any purchase, if you don't receive service or goods paid for, and the seller is non-cooperative or non- responsive, you go to the dispute process.
It's unlikely the Paypal transaction will go through if AA, as they have told you, has no booking to charge you for.
And I totally get it that this is a liquidity issue. So have your bank acct balance up on a separate tab and make sure you aren't overdrawing your acct as you make the purchase.
If you want to do belt and suspenders, call AA one more time, and have the potential Paypal reservation noted as invalid in case AA belatedly issues a booking against your Paypal "purchase.". You might want to have your new, valid PNR when you do this. Or maybe do the new reservation by phone and have the note entered then. This may not intercept a second booking using your Paypal purchase, but it will help when you insist that they cancel a reservation on what is likely a non refundable fare.
Maybe contact your bank and find out how they treat disputed debit charges, just in case you end up with two reservations, because overdrawing you acct seems to be the biggest risk here. Everything else - double booking, double charges - can get sorted pretty straightforwardly.
But really try to use credit for airfares. You're just way more protected.