Is it possible to prevent agglomeration and sedimentation of microparticles just by increasing the viscosity of the medium?
If you can make this, it will be stable. At equal volume of the phases, this will already be solid-like (0.5 is above percolation threshold, which is in the range of 0.25-0.3, depending on the geometry of your particles.). 

See https://en.wikipedia.org/wiki/Percolation_threshold#Thresholds_for_3D_continuum_models

The absolute particle size is irrelevant, only the size distribution matters. When you reach the percolation threshold, the only thing that matters about the continous phase is that it's incompressible, which is the case for practically all condensed matter. If it's viscosity is very low (and the solid particles large, > ~100 µm), it could flow out of the compound, but surface tension would usually preclude that.

Also a very lowly viscous continuous phase could mean that the compound yields already to gravity. https://en.wikipedia.org/wiki/Yield_(engineering) 

However it is not so simple to make such a suspension. If you try to mix powder and polymer, your stirrer (of whatever kind) will stop or break long before you get a homogeneous mixture, because your sample becomes solid, and there is no way of melting it or anything. A helper solvent can lower the solid fraction, below the percolation threshold, but is hard to get rid of later.

So you'll have to find out where the percolation threshold actually is, and just use a bit more. It varies a bit with temperature (your polymer phase will have a larger expansion coefficient, not sure if that is enough to make the difference). Anyway the yield stress is still tolerable just above the threshold, and processing is possible.