Your assumption has merit, if you have a specific size mixer and need a certain mixing intensity. If you need a moderate level of mixing intensity, and have a mixer with a specific impeller size and rotational speed, you will be able to handle a certain mixing volume for a specific viscosity. Of course, the motor and drive must be large enough to handle the load imposed by the fluid density and viscosity.

However, with regards to a vessel volume and fluid viscosity, only practical limits exist. For any vessel volume, most high viscosities can be blended with a properly designed and sized mixer. A larger mixer will be required for a higher viscosity. The opposite is more complicated. A given size mixer — established by impeller diameter and rotational speed — will only blend at the same intensity a certain volume of viscous fluid. The more viscous the fluid, the smaller the volume for the same mixing intensity, provided the motor and drive are sufficiently large.

The missing characteristic in your question is mixing intensity. Some blending applications require only that all of the fluid moves, while others require some minimum level of mixing intensity to be successful. The level of mixing intensity depends on the application. Storage applications may only require a minimum level of motion. Problems involving physical changes, such as temperature control of dissolving solids may require a moderate mixing intensity. Chemical reactions may require intense mixing for effective conversion. The mixing intensity is determined by the impeller type and diameter and the rotational speed. The impeller size and speed determine the amount of fluid motion possible. More initial fluid motion is needed to move more viscous fluids. Certain non-Newtonian viscosity characteristics make mixing more difficult than just apparent viscosity. The impeller size, type, and rotational speed, along with fluid density and viscosity, determine the amount of power required. A larger motor is only effective if the impeller size and rotational speed are appropriate to use the available power.

Physically, there is a relationship between blended viscosity, tank volume, and mixing intensity for any specific mixer. A larger mixer will effectively blend a more viscous fluid than a smaller mixer.  The mixer size must be selected to match the fluid viscosity, vessel volume, and mixing intensity.  No simple rule of thumb relates all of the different characteristics, especially since different impeller types give different results, in viscous fluids.