If it were that easy we wouldnyt bother with subs at all.
Its been done. In fact I worked on it back in the 1970s. rubber coated hulls, very slow propellors, down deep. Totally undetectable.
Same goes for thermal signature. You cant 'see' it through a lot of layers of water . And teh sub can run on batteries even if its a nuke,
I can assure you, they do, but I can also assure you, that a sub sitting at depth with engines off is almost impossible to detect. And there are limits to how much of the sea you can litter with sonobuoys.
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