I don't know the particulars of the AS-CX agreement, but based on what I've gathered from other airline partnerships, the short answer is: not necessarily. What an airline offers its partners for award travel is often (usually?) a smaller subset of what it offers its own program members for award travel.

However, checking availability directly with CX can give you a rough indication of availability, which can let you sort of lead the AS Partner Desk in the right direction for where they should look for availability.