I imagine if you knew those were codewords likely to appear in a cypher it could certainly help with cryptanalysis.

The opposite is true, actually. Imagine dealing with thousands of incoming data streams from spies, communication intercepts, and battlefield reports without the aid of computers. You have a classic needle-in-a-haystack data discovery problem.

Being able to communicate to your entire intelligence apparatus "hey send me everything you see about OMAHA or SWORD" might get you hundreds of small pieces of intel that would be too trivial to forward to command alone - but taken together could have laid out the entire battle plan.

The code words all being in the crossword is a sign though that you might have a serious information leak - perhaps not that the crossword was a secret message out to Germany.