My guess is "not necessarily." I recently used an AAdvantage award for F travel from the U.S. to BKK via HKG on CX. When I needed to change my return after arriving in BKK, I didn't think I'd have a problem based on past experience and the fact that virtually all upcoming CX flights over the next few days were showing "F4." In fact, it was quite difficult, and I found that, on average, only 1 of roughly 7 flights showing F4 had an award seat available. Both of the transpacific CX flights I was confirmed on had load factors of less than 50% in the F cabin. My impression is that these awards are significantly harder to book than in the past.