It's possible but a headache, carbs and cats don't mix well.
My Briggs & Stratton engined generator has a catalytic converter (apparently now required for CA) and a small carb but I think that works well as it's a narrow range engine- constant RPM, not a particularly variable load.
Lada used carburettors and catalytic converters through until the 90's, with enevitable problems as the carbs wore and got out of tune. They moved onto computer controlled SPI after that.
That being said, with the right setup and good conditions it's possible to "clean up" an engine- friend of ours had a 1977 Ford Fiesta with a 1.1 litre Kent engine, and a small Solex carburettor, mechanical CB points etc and it ran cleaner than a lot of cars WITH a catalytic converter, well maintained, with readings that had the tester check his machine on a few other cars to make sure it wasn't broken.
Best bet on an engine of that vintage would be fuel injection that can be mapped on a rolling road, to aid a 14:1 burn- but then factors like plugs and valveseats become an issue as you may end up burning the fuel hotter than designed (weaker mixture), especially with today's unleaded+ethanol.
I'd say go for it though, get the car running a good mixture and fling a couple cats on it, as close to the engine as possible to keep them hot.
Totally possible, and it would mean that "hulking dinosaur" need not be "scrapped"
--Phil