As wonderful as Turing's achievement was, I do sometimes wonder if it's the manner of his death that makes his story so popular. Perhaps too much so, to the detriment of the many hundreds of people who worked on the project to crack the Enigma code. The Polish mathematicians who started it all off, such as Marian Rejewski, barely get a mention.
In terms of the question -- it's almost unarguable that the work done on breaking German (and, separately, Japanese) codes shortened the War considerably and saved many thousands of lives. Perhaps even it shortened the war by a timescale measurable in years. Hugely vital work. No question about that. Turing's role in it was immense, to be sure.