Yes they will be able to tell for various reasons. Any basic engine swap even of the same capacity will require the new Engine number to be lodged so that it can be linked to the cars registration and chassis number. While during WOF inspections being basic safety and stability checks they may not always check the engine number against its chassis number but eventually someone will. Further more technically it would invalidate the cars registration and insurance and illegal to drive on the road and that may come back to haunt you if bad lucks comes your way. The problem is compounded by the fact that NZ laws are more stringent than most requiring Warranty Of Fitness (MOT to British readers, Pink Slip to Australian Readers) every six months for older cars compared to 12 months of most others increasing your risk of the engine number change being spotted. The engine naturally came out of another car and that engine number will be in their data base as a 1600 so one simple history check and your exposed basically.
If the replacement engine fitted is a larger capacity than that fitted originally it will require LVV certification (Low Volume Vehicle). This can sometimes be a stringent and repetitive process (in that you need to go back more than once) but it wont be in your case. Many of the other points that also require LVV certification your car meets easily. Engine mounting points, fuel type, Engine family similarities (In this case Kent engines) all work in your favour, adding to that the engine in question was offered originally from the factory in the Escort model line with the new engine capacity you have fitted. You can even increase power by 20% without requiring any certifications once the engine is cleared. You simply need a LVV certifier to sign off on it.
What you need to do is check out some of the LVV certifiers and chat generally with them and find the most amicable. Make it clear that this swap is simply another near identical Kent engine only with a slight capacity increase. Be sure to remind them (if they arent knowledgeable about older 70s Fords) that Escorts were fitted with these engines originally just yours was a 1.3 when it came out of the factory. Just suss them out in general and ask about the fees for that level of certification and find one that seems to know what he is talking about. In Australia if an engine was available in that cars product line from the factory it requires no special inspection just an engine number change through the Motor Registry. From what I have read New Zealand does want certification for anything over and above original capacity but its not mentioned if that's over and above for that specific car or its entire model line. I suspect its the former though and as such LVV will be necessary. I think there is a list of LVV inspectors online just ring a few and have a casual chat with them not giving away too many details that will identify your car specifically and let us know how you go. Good luck with it and welcome to the forum.