At least for moderate length rods (roughly 6 mm dia. x 30 mm long, often
seen in computer SMPSs), the change in inductivity is about half, so
you'll hardly notice it. The change is just as sharp as any ferrite
inductor though.
At an aspect ratio like that, you'll probably see more gradual saturation,
as the center becomes saturated first and the whole thing progressively
becomes an air-cored inductor.
Depending on what you're doing, rods often aren't wound all the way to the
end, because inductivity drops -- SWAG, fringing sucks down maybe half the
field out past 80% from the center. You occasionally also see multilayer
windings, which are great if the wire is thin, but only up to a winding
height about equal to the diameter. Think of the fields of a bar magnet,
they loop around pretty well from the ends, but any space within those
arcs is prime real estate for coil winding purposes.
Tim