Theoretically -- what would happen if I were to shut down / restart my CommServe (but not the media agents) while jobs are actively running?  I know no *new* jobs would start, but if jobs are actively running between a client and media agent -- would the commserve restarting impact that at all?

(FYI I say the jobs will go pending or error out, co-worker says they'll be find and keep running)

They can't run without the 'brains' of the operation in place. They'll go pending and restart once the CS is up and running again. The CS controls all the operations. 

If you've ever pushed updates to the CS with jobs running, same thing. 

One other thing worth noting, imho, is that jobs for some agents will restart gracefully (i.e. resume)  and pick up where they left off but others will need to completely restart from the beginning.  

VMware api backups unfortunately do not gracefully resume /restart from the middle.  

Windows file system jobs (and probably lots of other file/agents) may be able to resume/pick up where they left off, I think depending on settings.