I'm not entirely sure about this, but it was my understanding that if a block contains transactions that don't fit the fee rules, the block won't be relayed by most nodes, which would lead to a much larger chance of an orphan.
But how does that work, cause hundreds of zero-fee transactions get put into blocks at some point? What I am saying is this wouldn't have anything to do with the blockchain. You just pay a miner, a fee, so that they will include that transaction attached to the fee, in the next block they mine. Your paying a fee outside of the blockchain fee for a mess up.