Yes, but that 200 hours would be all training, mostly with some of the best instructors in the world, in aircraft that pushed him constantly. Plus, it was at a time when we had a very strong need to get pilots in Spitfires quickly.
That is very different to 200 hours in a modern and relatively undemanding GA environment.
It was obviously doable, since many young men in many countries did it at that time. But, I'd take a new PPL as maybe equivalent to 30 hours of that - so you're looking at 170 hours (ish) of robust training in demanding aircraft - leading up to reasonable hours in something similar to a Harvard, just as it would have been there.
That said, there's no need now to know how to fight a Spitfire, only to fly it so, maybe, you could bring that back to 100 hours. Maybe - but it would still have to be very demanding training.
Just as a semi-comparison, I fly in a syndicate a Stinson S108-2 which is a 1940s taildragger of WW2 ancestry, with a relatively small (165hp) engine and moderately demanding handling (certainly harder work than, say, a Cub - although just as fun). About 1 in 3 of PPLs who try to join the syndicate can fly the aircraft well enough to satisfy the rest of the syndicate that we'd trust them with it unsupervised. This is a much, easier aeroplane to fly than the Harvard or N3N-3 (both wartime trainers that I have flown) and from everything I've heard from reliable sources, the Spitfire is a much harder aeroplane than those.
G
N.B. Quick and gratuitous plug - whilst I'm very happy personally, a couple of our syndicate members are trying to sell their Stinson shares, so if you genuinely are interested in some warbird-ish flying, drop me a PM and I can tell you a bit more and put you in touch with the chaps trying to sell. Or chip in something for petrol and give me an excuse to go flying!