Would running this be the same as running 3 individual bitcoin in server mode for each computers?
No, if your server goes down the other 2 will not get any work to do.
but if you run 3 separate servers they will be competing with each other even if they each have a copy of the same wallet.
It's best to have the server be a stable non-mining machine or use a pool
I would personally connect to 3 pools and if one goes down the others could pick up the slack.