Yes, to a degree.
The endurance limit is normally expressed as a fraction of the yield stress and for steel a typical value is 1/2 (50%). This is is certainly a reasonable assumption for common low alloy, medium carbon steels ie the sort of steels that you might reasonably select for a shaft.
In fact for many practical purposes the factor of safety that you use to account for dynamic loading will be similar or greater than this anyway so it's often not a limiting factor in steel.
Equally for high performance, highly optimised designs you might not consider endurance stress as an absolute limitation and just design the part with a fatigue life.
And for really critical parts you relay need to consider the very detailed design in terms of surface finish, surface treatments and manufacturing processes as well as things like minimum radii when calculating fatigue life, for which tables of coefficients exist.
In general in engineering design optimisation is a process of getting increasingly confident about the actual real world loads a part will see, a process which is very much subject to diminishing returns and for general purpose deign it is often a case of selecting a sensible and pragmatic factor of safety in which you can be confident.
Response to comment by OP
It is mostly empirical. The difficulty with fatigue is that it is highly dependant on local stress raisers. As a bulk material steel is not very susceptible to fatigue, but you can easily get local stress concentrations eg around a surface defect in the wrong place which exceed the yield stress of the material and consequent work hardening over multiple cycles.
This isn't exactly the same mechanism as fatigue in say aluminium which has a very low endurance limit, even in ideal conditions.
As with many things in practical engineering it boils down to an empirical coefficient whcih is known to work for a given context.