I do the Sewbizgirl, rubbing my hand around to collect balls of fur first. Damp cloth helps with coarser cloth (like my dining room chairs), not so much on batiks.
Although I have done it, I really don't recommend washing a flimsy/unquilted top. Some spills or whatever are nasty enough to require that before finishing.
It's happened that something like this has motivated me to quilt down a top because I always wash them when I'm done and so I scrape off as much hair and threads as I can and quilt it down, trusting the after wash to take care of rest of it.
I try to keep my unquilted tops in large clear tubs to keep them as fold free and clean as I can until I get to them. Sometimes we don't find these cat nests until they've been used for quite awhile and it can be amazing the amount of fur that gets stuck to them, but usually it's just on one side/fold of the fabric and can be managed. Even dried cat barf can be managed... toothbrushes can help with this (the removal, not with brushing the cat teeth although that's not a bad thing to do either).
I have pets and I have pet hair in my house and on my quilts even though they aren't allowed in the sewing room. It's a fact of life that I am also covered with pet hair, and so I travel with those roller sheet things tucked everywhere. It's what the dollar store is for! I leave the house in the best shape I can and de-fur myself before getting in the car (keep a roller in the trunk just for that).