Flying CX on L/V class from LAX->SIN. What program: OW or MP?

Hi,
I am neither a OneWorld (AA) or Morco Polo member (my miles are in United/Delta). I am traveling on CP from LAX->SIN->SFO on a L/V economy class. Looking through the web pages of OW and CP, it seems like I would not earn any OW miles in this class. However, if I have MP membership ($50), then I will earn 1x miles for each mile flown in OW. Since I will be in the Green level, I would not get any other benefits - basically it is $50 for ~20K miles. Am I right? Since I fly neither airlines, I am not even sure what to do with those miles (I suppose I can try to fly AA in the future).

Thanks