Most batting can be soaked by itself but cannot tolerate agitation. The only kind I know of that cannot tolerate even soaking is old-fashioned 100% cotton such as Mountain Mist Blue Ribbon batting. Polyester battings, 80/20 battings, and cotton battings that are either needlepunched or needlepunched through scrim can be safely soaked (but not agitated).
I would probably replace both the fabric and the batting. It's pretty easy to baste batting together with a hand tailor-tacking stitch, with a long and wide machine zigzag, or there's even a fusible tape out now for this purpose so you can just iron the batting pieces together. To me, this would be the safest route.