I have both - I just tried it and the answer is no - the Clara is wider in the shoulders and differently shaped overall - it kind of sits on top of the depression in the case and slides around.
Have you considered or researched a Fremont case? For similar money you get a nice looking hard-sided case vs. polyfoam for the Fluke case. I have no idea how well the Fremont fits, but it does specify that it works for pineapple shapes.