I think the problem neither is pressure nor vulnerable structure of batteries.I don't think you're taking the immense underwater pressure into consideration.
If the pressure were problem they would not put there mini sub.
The problem would be lack of sterling engines. Li-ion batteries would need generators when the sub is underwater. Look at Japanese soryu class , they have 4 sterling engines ( which are noisy!)
Edit: sorry for false information. Last gen Japanese sub doesn't require sterling generator!!!
So do we have still chance ? No, because additional battery package would weight minimum 50-100 tons. This would disturb the balance of submarine.
JS Tōryū - Wikipedia
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