Nope, try it out:

  $ printf 'banana\ngrep banana\n' | grep banana | grep -v grep
  banana
  $ echo $?
  0
  $ printf 'grep banana\n' | grep banana | grep -v grep
  $ echo $?
  1

To clarify my previous comment, `grep -v grep` exits with 0 if there was a line without "grep" in the output of `grep banana`.