Mutation-immunity in Luria-Delbruck experiment
No. Surprisingly, there is an adaptive immune system in prokaryotes. This is still widely unknown. The newest review is

S. Al-Attar, E. R. Westra et al: Clustered regularly interspaced short palindromic repeats (CRISPRs): the hallmark of an ingenious antiviral defense mechanism in prokaryotes. In: Biological chemistry. 392, 4, April 2011, 277–289. doi:10.1515/BC.2011.042. PMID 21294681. (Review).

Cited from abstract:


  Many prokaryotes contain the recently discovered defense system
  against mobile genetic elements. This defense system contains a unique
  type of repetitive DNA stretches, termed Clustered Regularly
  Interspaced Short Palindromic Repeats (CRISPRs). CRISPRs consist of
  identical repeated DNA sequences (repeats), interspaced by highly
  variable sequences referred to as spacers. The spacers originate from
  either phages or plasmids and comprise the prokaryotes' 'immunological
  memory'. CRISPR-associated (cas) genes encode conserved proteins that
  together with CRISPRs make-up the CRISPR/Cas system, responsible for
  defending the prokaryotic cell against invaders.


and


  An application of the CRISPR/Cas system is the immunization of
  industry-relevant prokaryotes (or eukaryotes) against mobile-genetic
  invasion. In addition, the high variability of the CRISPR spacer
  content can be exploited for phylogenetic and evolutionary studies.
  Despite impressive progress during the last couple of years, the
  elucidation of several fundamental details will be a major challenge
  in future research.