Can An Engine Number Identify Registration Number?

Usually not. The number on the engine block is a casting number, which has nothing to do with the Vehicle Identification Number.
If that is what you are asking.

Registration number refers to who owns the vehicle.
There is a VIN number, which identifies the type of vehicle, the engine size, where and when it was manufactured.
If there is a number on the engine, it is usually an engine casting number and nothing more.

Wrong answer.  Yes, there may be a partial VIN on the engine block.  These have been stamped into engines by various manufacturers since the early 60s.  Over the counter blocks do not have a partial or full VIN as they were never assigned to a vehicle.  In some states, registration was by Motor Number, not Vehicle Number, although most go by the Federally mandated VIN attached to the body now.

There is usually an assembly number that has plant location, date, and configuration data stamped on the block, if the engine was assembled before being sold, as opposed to being a block sold as a part.

The difference is the partial or full VIN is stamped, meaning you can see how the number cuts into the metal from the stamp being hammered in, as opposed to the casting number which is usually a raised number that is formed when the block or part was cast.