From my understanding the transaction will hang around for some time, but most miners ignore malicious transactions like this so it is essentially discarded.

I believe you could resubmit the transaction after funding, I've seen people modify stalled transactions to include omitted transaction fees.

Are you "missing" BTC because you tried to manually push an invalid transaction? I think there is a simple command that should make your wallet recheck all your addresses, which would make the coins "appear" again.