All engines have serial numbers, however not all countries have links between the VI and serial number.
But probably what concerns you the most is if it is stolen or not. the answer is not simple, but it safe to assume that the origins will never be known but at the same time, are untraceable in the US or Canada.
This doesn't mean buying a foreign market stolen motor is OK, but there is no way to check them.
Here in Montreal, the Asian importers bring in containers of JDM motors for swaps but the serial numbers are useless for ID.

Personally, I am against people who do motor swaps with JDM parts, because this can only encourage thieves to keep the supply side up. Needless to say a bash the punks who install knowingly stolen domestic market stuff into their cars. It's a touchy subject however when your business is performance and racing.

Just my opinion.