I forgot about the concept of Block chain pruning. You are right, it might be best to send something to it.
Although, I don't think that a transaction with 0 outputs and a fee would be pruned. Then the fee would be lost.
It wouldn't. Once the fee has been transferred to a third address and that address is buried deep enough into the block chain it can be pruned.
The best would be to send a non-zero amount.