Can you turn on Invoice in advance of fulfillment feature for a specific subsidiary only? If not, what are the workarounds to do so?

I don't believe you can do it by sub. If you don't do partial invoicing, a workflow to hide the Invoice button until SO status is "Pending Billing" would be pretty easy. It would get trickier if you do partial invoicing because then you'd have to look at line items, which generally workflows aren't good at. You'd probably need a script at that point.