Local dark matter energy-density is very small, around 0.01 times the mass of the sun per cubic parsec or in SI units about 10^-16 kg / m^3. In concordance cosmology CDM neither dissipates nor collides, so it cannot easily clump into warmer (and brighter) dense structures, so it is always diffuse outside of black hole event horizons.

If we accept for the moment the existence of a pseudo-CDM identical to the concordance CDM except that it can interact with EmDrive microwaves, then the first question must be: why doesn't it interact with astrophysical masers in GMCs, affecting the structure evolution therein? (e.g., if astrophysical microwave hotspots move pseudo-CDM then there will be a bias in the location and age of young stellar objects and H II regions due to the change in energy-density). Some astrophysical megamasers have luminosities on the order of a thousand suns -- that's a lot of watts to shuffle dark matter around in your idea about the EmDrive, and that shuffling will drag dust and gas along with it.

Tweaking CDM into pseudo-CDM without it collapsing gravitationally by radiating photons directly or by colliding with charged particles is probably impossible for any but a tiny fraction of the overall mass-density of the dark matter sector. Collision or direct dissipation removes angular momentum from the particles such that they can fall a little closer to the centre of the galaxy. On a galactic scale, that leads to a much higher total energy density at galactic core at even fairly small fractions of the local energy density.

Avoiding that would require extremely demanding work and likely would have you adding a lot more new particles to the standard model to capture all the additional (broken) symmetries -- and it gets worse the greater the local energy density or equivalently the greater the interaction cross-section you require in order to interact with a physically small device like an EmDrive.