I always thought a payment can not go thru if it doesn't have at least 1 confirmation no matter how small it is.
Even below the miners fee.
When it has 1 confirmation then it is pretty sure that the transaction will stay. If it does not have a confirmation then slight risks exist. That's why exchanges at least demand 1 confirmation before they give you the coins you sent into your account.
This would not work anymore when the ones get their will that want bitcoin stay with 1 megabyte blocksize limit. Because then you can't trust anymore if transactions will reach and confirm.