That works except the In and Out is usually reversed; the In is on the right looking over the front of the softener's control valve, and the Out is on the left.
That's industry standard although Autotrol and a couple others are as you drew it; In on the left, Out on the right. IOWs backwards. So ya gotta look on the by-pass valve or control valve.
Of course you should be buying a softener with a Clack WS-1 control valve from me which is industry standard and the best choice for a DIYer.
I would go out the Out and up to the ceiling rather than going left and then up. It saves on fittings and tubing and reduces pressure loss. Support the weight of the plumbing, do not let the by-pass and/or control valve have strain on it.
You need a stop valve on the main line and preferably before the tee for the outside faucets. And one past the tee so you can shut off those outside faucets. Most by-pass valves today are separate ball valves on the In and Outlets of the by-pass valve. IF you turn the In side by-pass valve to by-pass, that shuts off all the water past the softener. Shut the Outlet too, and the softener is by-passed and the house gets hard/raw water.
So no manual three way by-pass valve type by-passes are needed.