No, just the right part number. On any full blown resto or even getting a fresh engine, I always get the rad done. Sometimes it can be hot tanked and repainted, but most of the time there is core damage and it needs a recore. There's no way I'd trust that rad with a fresh motor.
Find a good radiator shop and have yours hot tanked and go from there. There are better cores out there than the stock ones as well as some inferior ones. I used a "high performance" 3 row core on my original 22" rad. The tanks can and should be saved.
Cheers,
Dave