Of course you can. Try Redux + websocket : its awesome !
Client side : UI Action -> dispatchAction -> update the Store -> UI rerender Server side : WS request -> dispatchAction -> update the Store -> WS response
And when you have both : UI Action === WS Request -> dispatchAction (ServerSide) -> update the Store (Server Side) -> WS response -> update the Store (client side) -> UI rerender
For that, you can use middleware to dispatch automatically wsrequest on ui-action and save the new store automatically on wsresponse. Easy !
With this you can have a easy synchronized client/server store tought the time.
The only one problem, is how to scale with websocket ?
Cheers !