Priority is based on current time not the time of sending. So yes the priority will slowly rise.
Many miners include no fee transactions HOWEVER as an anti DOS prevention measure they only include no fee HIGH PRIORITY tx. Your example tx is low priority. You can't even send that without patching the client or creating a raw transaction. Most nodes will refuse to relay it and most miners will refuse to mine it.... until it becomes high priority in ~410 days.
It is important to remember there are essentially two fees in Bitcoin although they are lumped together:
a)
min mandatory fees on low priority tx - these are essentially anti-spam rules and don't exist to generate revenue (the amount of revenue they would generate is negligible). The purpose of these rules is to prevent an attacker from destroying the network at negligible cost.
To avoid this requirement your tx must meet the criteria here:
https://en.bitcoin.it/wiki/Transaction_feesIf your tx is doesn't meet the criteria to bypass the min mandatory fee AND you send it without a fee it is highly likely it will never be included in a block as any node running unmodified bitcoind will refuse to relay/mine these tx as a security measure even if there is space available in a block.
b)
optional fees. fees paid on high priority txs (which don't require a fee) or fees paid in excess of the min mandatory fees. Users include these fees to increase the likelihood a tx will be included in the next block. Since miners prioritize tx in the memory pool based on fees paid a higher fee in theory means faster inclusion in a block.