What I mean is, the transaction won't sit there until the public address is funded, correct?
Bitcoin doesn't work on the concept of "funded". A tx consists of specific inputs which are prior tx outputs.
If the inputs are invalid or already spent the tx will be dropped by the first nodes it is sent to. You can't later fund the "address" because Bitcoin doesn't work on the concept of an address having x BTC worth of "funds". Sending funds to the address would create a brand new input, one not referenced by your prior invalid tx.
Simple version:
Invalid tx are simply dropped.
Unconfirmed =/= invalid it just means not included in a block.