Of the 5 pilots I know that fly with Cathay, none of them have a degree. I know of 1 in DragonAir, no degree. Also know of a couple of guys in Singapore Airlines with no degree, but they were direct entry Captains with a bunch of jet time prior to getting hired.
All of these guys flew GA for a number of years, all had turboprop experience and averaged more than 3500hrs total when they scored their interviews. Worked out well too, all are flying either 744 or A340 with CX, and A320 with Dragon!
Something to note though, Cathay have just raised their minimums to 3000 total, 1000 turbine.
The Australia/Asia region doesn't seem to worry too much about what you decided to do after high school. As long as you have some good quality flying experience under your belt and you are able to pass the ATPL subjects, you are fit for an interview. The interview and sim check will be the judge on whether or not you get the job.
The degree seems to be the essential part of getting to the majors in the US, but not such an important factor in the Southern Hemisphere. Down here, although it doesn't play a part in getting hired, it is definitely something that should be considered. A degree is something good to have should aviation not work out for you.
By the way, what sort of flying are you currently doing out of Sydney?