If you put it in the washer, the "spin cycle" should take 95% of the water out of it. When you lay it on the back of the sofa, lay it with the good side facing up and stretach it out. give a quick swipe to each pleat to help them dry "straight" to make your ironing job much easier.

It shouldn't "soak" the sofa, but if getting the furniture wet at all is a concern, then I'd suggest hanging it up on 2 or 3 hanger (again, open if possible) somewhere in the house or on a clothes line.