I know little about mass spectroscopy. However, years ago, people who know a lot told me that EDX does not work reliably with samples of material such as powder or other particles not compact or electrically conductive.
I think that is an unfair characterization of EDX. If you can image with the microscope, avoiding charge build-up, then EDX will in general be a reliable indicator of what elements are present. EDX will only provide an approximate measure of composition ratios and really provides no information on molecular structure - just what elements are present. To deal with charge build-up, many SEMs will have the chamber at an air or argon pressure of about 7 torr, compared to the normal ultra-high vacuum that must be maintained in the column. This prevents measurements of secondary electrons, and of course, you may detect oxygen, argon, and nitrogen in the x-ray spectrum.
Most samples are placed on a conductive carbon sticky tape which will cause carbon to show up in every analysis - sometimes a lot. This makes it difficult to determine if carbon is really in the spot probed by EDX or not. Generally, you have to ignore the carbon in the analysis.
Also, EDX works by having the electron beam knock off electrons from the atom and when the electrons are restored, it gives off the characteristic photon spectrum of the element. The characteristic photons of low atomic weight elements are very low energy and don't make it through the window on the x-ray sensor. You need a special x-ray sensor window (polymer) to be able to detect down to boron (Be windows are more common). Seeing Be or Li is nearly impossible with any sensor window - you need a sensor without a window and a high vacuum system to seen Be or Li.
There is a caveat: if your sample is radioactive, it can generate spurious lines in the acquired x-ray spectrum that are not the characteristic lines of anything. The analysis software may not deal with these extra lines gracefully and may say that an element is present that is not actually there. I have never seen this happen.