The Ostwald Viscometer is a comparator (with water usually). It is hard to see how the shear stress could be varied to examine Non-Newtonian behaviour.
as Jack Broughton said, the Ostwald viscometer will only give you one viscosity point for a sample that has a shear thinning nature ie, it‘s viscosity changes depending on the shear rate. So that viscosity value may or may not be at all accurate for your needs, but rather only represents the viscosity across a narrow stress range (as it’s a gravity driven system).
Broughton and Rolfe gave relevant answers. I suppose one could use the Ostwald viscometer in a centrifuge to change effective gravity. Might be worth researching.
Poorly: for a given, however unknown, shear rate (or deformation rate), it would give the apparent viscosity of the non-newtonian fluid.
Note: strictly speaking, viscosity is the name of a physical property characteristic of newtonian fluids. Then, apparent viscosity to avoid confusion..
Isha Arora Viscosity can be defined as the ratio of local steady state shear stress to steady state shear rate for viscometric flows of any nonNewtonian fluid. One simply cannot say "the viscosity" since it is not constant. No need to say "apparent" which borders on pleonasm.