Just to be clear: Let's assume KtD's stats are correct, and only 1% of the QBs picked in the 6th round are successful in the NFL (by some agreed-upon measure of "successful"). One might reasonably make the case that, any random QB picked in the 6th round has a chance to be successful, based on past experience. But that means very little when it comes to the chances of a SPECIFIC QB picked in the 6th round.
Also, there isn't necessarily a causal implication between "round 6" and "success". But mannc makes a decent point. There might indeed be some causal connection if "round 6" also means, fewer opportunities, less coaching, etc.
From a practical standpoint, QBs who look ready (or like they have the potential to be ready in a reasonable amount of time) for the NFL, rarely last the 3rd round. Indeed, most of them get swiped up earlier. But I think, with the right resources and mind set*, more later round QB prospects could achieve some success in the NFL.
*This refers to the drafting organization, but probably also extends to the player himself.