Will the Qproteome Plasma Membrane Protein Kit work with starting materials other than adherent mammalian cells?

No, the Qproteome Plasma Membrane Protein Kit was developed for adherent mammalian cells. The ligand used to recognize mammalian-specific plasma membrane structures will not recognize cells or structures from non-mammalian organisms, such as e.g. plant cells, yeast, cyanobacteria, chloroplast thylakoid membranes, etc..