No. We're talking about people with no respect for the system in the first place, and are expert at working around it. The only thing that will change is the number of illegal immigrants. It will increase.
How many Mastercards are there floating around with your account number being used? These cards should also be tied to a bank account and the access to their payroll checks. The banking account number is set up with many checks that can be refined as time goes on. A counterfeiter who would try to use somebody's number would generate a termination order. That would require someone to go back to their home country and get a new card. Not a happy prospect. The countefeiter would be severely punished if caught. There are many ways that could be used to safeguard the system. I am not really as good as the experts.