No it wouldn't.  Miners connect to the node (just like they do any node running p2pool) over TCP/IP.  The mining software is on the miner.   Instead of pointing it at a pool wallet you point it at your p2pool node, exactly as you do now if p2pool is running on a desktop.

As for not useful well that depends.  Just as a hardware which runs a full node for the network and does nothing for the user well your right that is beyond stupid.  Why would one buy one?  However how about this.   Your wallet is on your computer, you don't want to run bitcoind locally for a couple of reasons such as you have multiple computers running bitcoind on all of them it excessive, or you don't use your wallet everyday and hate the fact that when it syncs up you need to wait.

So instead you use a light wallet which connects to your local bitcoin node (running on that <1W device connected to your local network).  Got 8 wallets spread across multiple computers no problem they can all point to the same local bitcoind.  Now you could use a SPV client but maybe you don't like the security compromise and the fact that it doesn't strengthen the network.