I did SFO to BKK (with a stopover in Hong Kong) on CX recently using AS miles, and it worked well. CX has something like 7 flights a day from HKG-BKK, and I found it was the North America to HKG leg that had more limited availability.
One word of warning: you cannot search for or book a CX award ticket online with AS. The partner award desk folks are very helpful, but it's still annoying and somewhat tedious to have to search for availability over the phone. I did find, however, that the award availability shown on CX's own website roughly correlated to the availability that AS had.
Finally, I would seriously consider booking in business class. It's only 40,000 more miles (i.e., 100,000 total), and well worth it in my opinion. CX's new business class on the 777-300ER (which they use for LAX) is great!