CX to my knowledge doesn't care where you got your license from, so long as it is legal, and you can demonstrate to them you can be competent at the job during your interview. If you are keen to join CX and don't have a license yet, then just go for their cadet program. I wouldn't go out and get a license just to join CX.
If you do go out and get flight training elsewhere, then I highly recommend building your experience from elsewhere. Learn to work your way up, fly some turboprops, and regional flying. It will be a much more rewarding career than going straight to cruise relief on a long haul wide body. Some guys at CX have never done this, and they have missed out on the fun.
As you can tell from these forums, CX is also not the same airline it used to be. There used to be a time when I think people used to be proud working at CX. The days are long gone, and I can assure you the attitude is not just a forum thing. You must recognize that in between CX making financial losses, and the expensive nature of Hong Kong, that CX is trying to make consessions out of the pilots. I'm not saying CX is going to be a bad employer forever, but do be wise in your career decision making. You only get so many chances.
I say this from hard learned experience.