Modern Navy ships (gas turbine) with dual shafts do this all the time. During normal cruising, either the port or starboard shaft is being driven by a single engine (each shaft is coupled to two engines). The offline shaft spins freely with no engines on line. This plant alignment is called "Trail Shaft" and it is very efficient.
Obviously there are differences here, but the point is that trailing a propeller still uses less fuel than having two shafts online.
How fast the trailing screw turns will be a result of the vessel's speed, obviously. But the Navy does not lock the shaft. As the trailing screw turns, drag is reduced. If you aren't going fast enough to turn the trailing screw then drag really isn't a concern in the first place.
Now, whether or not you should lock your shaft is a question of how your gearbox is made. Your manufacturer can answer that question. But as to drag, the trailing screw free wheeling is better than being locked in place.
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