Come off it! How does this solo pool get paid? If you find the block, then you get 99.95% of the 25 BTC it is worth, the rest to the pool.
In the same breath I'd add, the "normal" pool mining would say incur a flat rate for paying out to your address (not rocket science, but the pool gets paid then!)
But I digress, the question was is that kind of pool technically feasible to implement (or am I barking mad because that is what P2Pool is)?
You're asking if work can be submitted twice. It can't. Think about it. If something like this could be implemented, then I could take my hashing power and multiply it by connecting to multiple pools. So, in pool 1, I have 1TH/s, and pool 2 I have that same 1TH/s, and in pool N I have my 1TH/s, effectively giving me N TH/s mining, when I only have a single terra hash of hardware. So, to answer your question, no, that kind of pool is not technically feasible to implement.
P2Pool does nothing of the sort. P2Pool has its own block chain called the share chain. Each share that is added to the chain either solves the BTC block or it does not. If it does, the generation transaction includes the payouts to all the miners who have shares on the chain. If it does not solve the block, it is just added to the share chain.