I used CMlink China number opened China Bank account. And so far with no problem.
I was able to send verification SMS at CMlink Singapore webpage in Singapore. (Just now I logged into webpage, and found the layout of SMS sent page is changed. Previously, only certain China number can be send, now it looks like no such restrictions, may be now need to put +86 in the front to send SMS?)
When in SG, this CMlink CN number can receive call from China for free, and it is integrated to the same SG SIM card. But if it is a China CN number, it will be charged with IDD call if answer Call from China and send SMS to China. And need separate SIM card.
Can login into China mobile APP(mainland China) with CN number. It is nothing to do with SG number, it only tells that Chinamobile has this number.