In my experience it's rare for CX to provide award availability to partners. It's the same pain with BA. The only thing you can do is to check as much as you can.

There's a chance it'll appear but it's not guaranteed.

If you want to secure it you'd probably be best booking through CX (although Avios will be useless - you'll need Asia Miles and CX is a bit less flexible with their redemptions compared to QR).