Attach a double sided tape on sample holder. Carefully remove the upper cover of the tape and spread powder sample, so that almost a mono-particle layer is formed on it. Then apply a mild press on the sample using the tape-cover paper, which ensure attachment of the particles to the surface. Now, coat the sample with carbon, Au or Pt. Sputtering time, applied voltage, current should be set at optimum level of the coater. Coating layer thickness should be < 5 Angstrom. For better distribution of the particles in the SEM sample, you can make a very dilute dispersion, then spray it on a thin mica sheet, dry it well in a vacuum desiccator, coat it to make conducting and observe the coated sample with SEM.
In SEM you will see the film with which the powder is coated. This information is useless to you. You are better off making IR or Raman spectra of the powder with and without coatings. Comparing the change in the fingerprints of functional groups, you can get interesting conclusions about the interaction of the coating with the powder.
If you use KBr pellet you might have scattering problem using IR if you have microparticles but not if you use a micro-Raman. You can always use ATR-FTIR to avoid the problem. This would tell you if you have polymer in the sample (not necessary if that polymer is where you want it to be).
Maybe you could use backscattering SEM to check if you have organic on the Mn particle surface or use a transmission technique (TEM or optic microscopy if both particles and shell are tiny or big enough).
Also an Mn quantification might help to know how mich of your final mass is MnCO3 and how migh is possibly polymer.