You need >50% of the computational power to get 6 confirmations. For 1 confirmation, 1% of CPU power will give you about a 1% chance of being able to reverse the transaction, regardless of how well the original transaction propagated.

If the attacker can't do that, then broadcasting and waiting a few seconds does give a good chance that there will be no double-spending. However, nodes will not relay transactions they consider bad, so you might not see bad transactions until they're in a block. This is why a centralized "super node" with many connections is desired. And Bitcoin doesn't currently warn you about double-spends, anyway.