Yes, you can. If the AI actually has radar coverage in the sea zone and naval bombers, even '44 subs with snorkel 2 will be ground down fairly efficiently, to the point that I have to withdraw. You can't completely protect the subs with air cover either, because naval bombers slip through often enough to deliver a deadly blow.I was under the impression you could see '40 subs and kill with drop planes + radar + air superiority pretty easily, and once spotted destroyers or NAV can put them down.
I most often run into this problem when taking on the US in WW3, where I just have to stay out of Florida coast with my subs until I take care of the bombers. The way I take care of the bombers is by building destroyers which are basically floating AA batteries, and sending them out to lure the bombers to try to bomb them. Coupled with fighter cover, the naval bombers eventually get all shot down, though it takes a long while. That's one of the few times when I build something other than subs for my navy.
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