One thing about water is that it finds the path of least resistance. The water may be coming from a different leak but finding its way out through the same path. Is it possible to move your cabinets to a different wall?
I would think that your homeowner's insurance has a general "home/personal contents" coverage where what ever may be damaged can be pigeon-holed, but certainly you should have your more expensive machines listed specifically.
As to your original question, you don't know where the water is coming from and what is in it. Drying it could set whatever minerals/particles may be in the water into the fabric and cause staining. I would wash it first just to be on the safe side.
Sorry you are going thru this again. How frustrating it must be.