not if priority is greater than 57600000, according to the official wiki.
There is a lot of competition for the free transaction area in blocks these days; you need a much higher priority to get confirmed quickly, 57.6 million is not enough any more.
This is important to keep in mind (and it a reason I pay the "min fee" on all tx even those which may qualify as "free"). To the OP the priority requirement is merely the requirement imposed by nodes to relay tx without a fee. Once it is relayed to a miner how long it takes (in terms of # of blocks) before it is included in a block will depend on the relative priority of other no fee transactions. If ranked by priority you are #1 then you probably are going in the next block (although some miners don't include any unpaid txs) if you are 1,000th and the average miner puts 20 free tx per block you might be waiting a while.
Still if it helps the priority requirement is "One Bitcoin Day":
If you receive 1 BTC and hold it for one day it will have enough priority to be spent without a fee.
If you receive 0.01 BTC you would need to hold it 100 days before it has enough priority to be spent without a fee.
If you receive 144 BTC and you would need to hold it for 1/144th of a day (1 block) before it has enough priority to be spent without a fee.
