In the case of my great-great-grandfather, it apparently worked.  In the town hall in Chęciny, I found his death registration in the 1940 civil register, illustrated above.  He lived to age 85, under the Nazi occupation.

But again, make no assumptions — there are cases in which a baby was named Chaim (or Alter, Zayde, etc.) because he or she was named in memory of a deceased relative with that name.  (For example, my uncle, born 1945, was named "Alter" in memory of this great-grandfather who died in 1940).