I've never heard of a process server being attacked for doing his or her job. That I know of, it is not really an inherently dangerous job. When was the last time you read about a server being attacked? People don't like being served, but shooting the messenger is really not a common practice.
Serving a summons or other legal document does not override California's codes, so I don't see what the point of using that as any added special need for CCW. Personally, I think taking a gun with you during service of process might actually cause the recipient to fear you, whereas going with papers only at least you don't elevate that spectre