It will definitely help. Investigators will have some bread crumbs to follow when a mobile phone related crime is committed and even when the documents used are forgeries, there will be some clues left behind which police can act on. Right now, investigations are almost impossible.
I think it will deter some but the hardened type who are ready to risk getting caught if the pay off is good will not be deterred at all. KYC requirements have not deterred bank fraudsters but if you think about it, there is always some clues left for investigators should they choose to look hard.
I am also sure it will be a Godsend to intelligence guys. Cellphones are used to communicate to many people, not just to victims. They will call friends, accomplices, service providers, and generally mention things which can point investigators in the right direction. Again all this contingent on the police/NSIS choosing to do right thing and assuming no one greases someone's hand so they look the other way.
My two Zim cents worth...
Great men are not always wise, neither do the aged understand judgement...