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You switched from cordless drills to mobile phones and lost me.
If no phones are involved then yes. Your setup should word if I have understood it correctly i.e.
Have charging cradles at home to charge the 16v batteries. And install identical cradles wired in parallel to the lead acid battery. So you bring your batteries and plug them in to your car and off you go.
Should work but I see a tiny problem. As the batteries have a higher voltage than lead acid, they will constantly waste energy over charging your lead acid battery. Swapping the lead acid with capacitors would solve this issue.
Is your intention to go alternatorless or over volt the system so the alternator is effectively disabled.
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