Blood viscosity is altered in some diseases such as sickle cell anemia, but there are other quicker and easier assays to identify many of these pathologies.
The mechanical properties (Viscosity) of blood are very much influenced by the patient’s health. In fact, various diseases change the blood rheology such as diabetes, myocardial infarction, hypertension and rheumatic diseases. The increase in the blood viscosity might be due to an increase in blood’s cholesterol levels. The cholesterol levels are not constant throughout the day, as after a big meal the levels rise and after sleep the levels lower. Since an increase in cholesterol levels mean an increase in blood viscosity, there is an inherent uncertainty in blood viscosity for a patient on a daily basis.
In computational hemodynamics, usually the blood flow is modeled by Non-Newtonian model (e.g. Carreau–Yasuda model), where the non-linear relationship between shear rate and viscosity could be established. Then, the wall shear induced by the blood flow imposing on endothelial cells can gradually change the alignment of the cell pavement and trigger some pathology of atherosclerosis. Thus, the viscosity modelling plays an critical role in computational hemodynamics.
Therefore, the rheological properties of blood is very important in prediction and diagnosis of atherosclerosis and other vascular diseases.
The blood do have a yield stress as it is not completely liquid!! It has many particles and proteins flowing along with it, it is a two-phase material other than being just a liquid. Since, the blood cannot be assumed as a normal liquid and It will sustain some small stresses.
Going back to the main question, Since our cardiovascular system has an active equilibrium i.e. Homeostasis, it will react to any changes made to its components or environment and will get to a new equilibrium, trying to minimize the effect of this changes. As a result, any alteration of the system parameters (and blood's mechanical properties as a system component) is an indicator of pathological changes of the system. Continuous monitoring of this parameters will lead to diagnostic methods.
The only issue regarding this type of diagnosis is that you should have the minimally invasive instruments to measure this parameters. This is where emerging needs to use MEMS in modern medical pathology comes through.
Blood viscosity, as mentioned earlier, can be influenced by many factors and therefore any measurement of the viscosity can only be used as a tool to aid in the differential diagnosis of a constellation set of disease states. For instance, polycythemia will increase the viscosity whereas anemia can lower the viscosity. Leukocytosis as well as thrombocytosis can increase the viscosity whereas leukopenia and thrombocytopenia will lower the viscosity.
After that being said, the meausrement of the viscosity would definitely be an important indice to meausre for various disease states and even to monitor for the progression of disease states in real time.
Red cells (which have structural boundaries) have a structural (not material) yield stress (at which elastic (reversible) deformation ceases and plastic (irreversible) deformation begins. Blood (although it contains cells) is a liquid. I can't find any literature reference claiming that blood undergoes elastic (reversible) deformation--except by confining it some space, giving it an artificial boundary. Therefore, blood per se cannot have a yield stress in the generally accepted sense of the term. See: https://en.wikipedia.org/wiki/Yield_stress
The problem is that workers in this field have chosen to designate as a "yield stress" a phenomenon they observe while studying dynamic viscosity of blood. I think that is unfortunate because yield stress is a well-defined property of solid materials. I think they should have stuck with the true description of what they observed (quote from reference below) rather than re-naming it yield stress:
"Measurements at still lower shear rates would be of interest because they would provide information on blood critical threshold of stress, referred to here as blood yield stress. This critical threshold is representative of the formation of a weak percolating physical gel. "
Blood yield stress in systemic sclerosis Picart, Catherine, Patrick H. Carpentier, He´ le`ne Galliard, and Jean-Michel Piau. Blood yield stress in systemic sclerosis. Am. J. Physiol. 276 (Heart Circ. Physiol.45): H771–H777, 1999
To account for blood's yield stress is yet debated as far as I'm concerned. From a direct clinical application point of view, however, blood mechanical properties are rather important. For instance, mechanical properties of blood vary significantly from a renal failure patient to another during chronic dialysis as the hemodialysis machine pump cause mechanical trauma to individual red blood cells. As a result, drastic hematocrit changes throughout the treatment duration is prevalent due to blood rouleaux formation and etc. in these patients.
In modern era translational medicine, blood mechanical properties are taken into account via viscometry tests and implementation of constitutive relations such as Casson, Quemada, Walburn-Schneck,... to monitor patient-specific viscosity variations in time and to modify the demographics of the treatment accordingly to ensure dialysis success. My Master's and PhD thesis is on this topic. Hope this helps!