I think so. The court can order them to release the children pending an appeal, but it isn't likely they will. Usually the appeal will halt any further changes until it is heard by the court. But they will have file within that 10 day period the appeals court gave them.
IE, Texas pulled the kids, the FLDS filed for an appeal and the kids remained in custody. Now the appeals court has given them 10 days to return the kids. If they file the appeal in those 10 days then everything goes on hold again. If they don't file within those 10 days, the kids will have to go back to parents and things will hold until it is heard farther up. At least that is my understanding of it.