The rest of the network (well decided on a node by node basis) may refuse to relay your tx however if you hash a valid block then unconfirmed double spend or insufficient fees it will still be accepted by the rest of the network.
An unintentional double spend can happen like this:
a) you create a tx with 0 fee using input A. It is rejected by some but not all nodes. It is relayed to miners but none include it in a block determining it is invalid.
b) you reinstall bitcoin and restore a wallet backup. you create a tx w/ fees using the same input A. The miners which relayed tx a) above won't relay this one because they see it as a double spend of the same input. If enough nodes refuse to relay it you won't be able to reach a miner.
I would also point out as long as your bitcoind is running it will continually try to rebroadcast the tx (until it sees it in a block) which means the network will never forget about it. So if your no-fee version is still running the network will never forget about the 0-fee txs.