Yes. The GC (or LC) will not be able to handle whole cells, or fragments of whole cells. Also, some things, like portions of cell membranes, or complete organelles are too complex a mixture to be easily fractionated on the GC -- even if we ignore the fact that they're often not very volatile. And furthermore, will rapidly clog the skimmer cone (substitute the name your MS manufacturer uses for that part) with stuff that failed to ionize because it was just too large. You will have to look up procedures similar to what you're looking to to to determine some method of clean-up.
Now, analyzing proteins, oligonucleotides and lipids on MS is done. But they have to be in a dispersed solution, often the output of an LC. There are deconvolution algorithms, which back calculate from the fragmentation the parent ion (which generally never appears for large biomolecules) and also user-built databases that can use the fragmentation data to predict structure changes in large biomolecules. But those applications are specialized, and a vendor can help you with that.
I don't know if you want to be able to do both, at the same time, on the same instrument. But that may be too tall of an order to be practical. Or maybe not possible.