I have not been able to upgrade from MEL-LAX, but I certainly have been able to upgrade for US$550 from LAX-MEL. I have done this a few times now. As said by others previously, it really is a cough shoot, but well worth a shot. 
 
Most times they have seats that haven't been taken up with upgrades, so from UA point of view it really is a good move to take an extra few hundred dollars that they would not have normally had.