Because each of the species used in this VOC summation has its own molecular weight (which you can view in the second column of the GC_{mech}.nml file), there is no unique molecular weight for VOC as it would depend not only on the molecular weights of the individual species but also their relative abundance which varies in space and time.
This is the reason that ppbC is often used when working with a sum of individual VOC species/compounds. Each of these species/compounds has one or more carbon atoms, and the molecular weight of those carbon atoms (12) is of course the same across species/compounds. So multiplying each mixing ratio with that carbon number when creating a “VOC” sum in ppbC yields a quantity that focuses on the aspect that all of these species/compounds have in common. This quantity can also easily be converted to ugC/m3 by using the molecular weight of carbon.
All that said, whether and how summing across mixing ratios of different VOC species/compounds is useful or desirable really depends on the objectives of a particular analysis. When comparing to measurements, for some specific species/compounds it’s also important to consider if the chemical mechanism used in CMAQ follows a lumped-structure approach to species aggregation like CB6 or a lumped-molecule approach like for example SAPRC, but this goes well beyond my area of expertise. You might also want to read this recent discussion on different ways to think about VOC.