We had a similar leak in our house and it got into my fabric. I didn't see it for a couple of days. Some of the cabinet parts looked dry until I took everything out and saw that indeed there were wet spots that mold was actually starting to form on. Ugh. Water damage was also under the cabinet and behind. I washed everything and treated the cabinets to blown heat for several days. (A bathroom heater) (Advice from my insurance carrier)
I know it is a big job, but I would take everything out just to be safe. Sorry this happened to you!

By chance is your picture dated? That would really help out with your insurance if it is. Maybe they will pay for lost fabric. I have no idea. Makes me think I may need to take a pic. of my fabric. I took one last year of my machine and have it on computer as well as still on the camera, because of burgularies around at the time.

I never thought of taking pictures of my stash and machines. Thanks for a great idea!

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.

I am sorry you are going thru this with all of your cool fabrics, I hope you found the leak and got it fixed now

take care and hugs