We had an Alfa like that. We asked the customer if the vehicle was fitted with it's original ecu and he said "YES" We have only fitted the Bare engine. So After checking the vehicle over, We found out that the ECU was for a different engine, ( They had fitted the wrong engine, 1.8 instead of 2.0 ) So I asked again, Are you sure that you have fitted it's own Ecu. ?? So he said where is the Ecu. ?? So I told him that it was the Small alluminium block on the top of the engine, And he said. Ohhhhhhh That thing, I thought that was a Multiplug where the engine harness plugs in.
ERRRRRRRRRRRR. It's still on the old engine out in the Yard. >
So we fitted the original ecu and it ran. ( Although it ran crap as it was now a 2,0L Ecu running a 1.8 engine )
So To answer your Question. As has already been said, If The "original ecu" was fitted to the Replacement engine it should run without a problem. If the engines own ecu was fitted then it will need matching to the immobiliser.