Because many mito-targeted drugs rely on membrane potential, I am wondering if I should treat adherent cells before or after trypsinization, with flow cytometry being the final method of analysis.
Even if the treatment of cells with EDTA-trypsin and analysis solution of CytoID kit, it would not bring trouble if you treat all the samples in the same way. If you really avoid the relative analysis of mitochondrial membrane potential, it would be better to perform fluorescent immunohistochemistry.
This is easily determined by you with your cells. The ester form of the compound TMRM is cell permeable and is activated (given a charge) in the cells by a host of esterases. If the mitochondria are charged (polarized IMM) and have not undergone any type of mitochondrial permeability transition then they will retain the TMRM. Is is often descried as the TMRM is "electrophoreticlly" retained. here is a link to the dye.
As Drs. Wong and Pediaditakis say, it is better to test it experimentally. Being TMRM and flow cytometry a semiquantitative method, it is not easy to compare using flow cytometry adherent cells vs trypsinized cells, but a confocal approach should be able to solve your question. Also, use an uncoupler like FCCP or CCCP to set a "zero" MMP and valinomycin/K+ to set a standard curve, That would help to to use standard methods in both types of cells. Undoubtedly, there are assumptions in these methods, but applied to similar cells I think they can be trusted as acceptable.