I am not aware of any effect of aspirin on blood viscosity (and I'm not sure why anybody would study that to be sure one way or the other). This idea may come from the inaccurate common parlance of "blood thinner" to describe anticoagulants. Aspirin's primary effect is to inactivate platelets, which are one arm of the blood clotting mechanism. When there is a need to clot, platelets become "sticky" and clump, helping to form plugs in the damaged blood vessels. After aspirin, they are unable to do this.
The physics of gas absorption and eliminate are related to the fluid phase of blood (the water component) for the most part, with the exception of oxygen uptake and transport. (That's a simplified statement, but it will do.) I can't think of any reason why aspirin or any other anticoagulant would affect this.
A diver taking aspirin would be somewhat less likely to have an underwater heart attack or stroke, but more likely to bleed heavily from a shark bite