My Roadster did not have a 12v battery. The 12v was just supplied by stepping down part of the main battery. Even if you ran the main battery down to 0 miles it still worked because there was a separate section of the battery used. I worked just fine. Later Roadsters went with the 12v lead acid battery. I would think that if they wanted a separate low voltage battery they could use a lithium pack which would have much longer life and be more reliable then a lead acid battery (and be lighter also).
You can definitely do that but its more expensive than lead acid. There are several Lithium variants that work fine as a 12v replacement.
The only one on amazon is
Amazon.com: Braille Battery ML7S 12 Volt Lithium Battery: Automotive at $400 and it's only 6ah. Too small for a Tesla.
You'll see most lithium 12v car replacement batteries much larger than that and all well above $400. Even if Tesla gets a discount or spends the R&D to make their own it will be more than double the cost of lead acid.
Cheapest at
12 Volt Lithium Battery is almost $600 but at least it is 40 ah so you know it's big enough.
advance Auto has one that is 14ah for $150, just not sure if that is enough for a Model S, might be better than the current 12v, might be similar (lead acid works OK with 50% depth of discharge, most lithium 12v replacements are good to 80% depth of discharge so you don't need as large a nameplate capacity to have the same usable capacity). I don't know enough about the vampire drain vs 12v capacity to make a judgement if that is enough.
Oreily auto parts doesn't have any lithium 12v replacements
Autozone is the same, nothing there.
Overall lithium 12v replacements are a darn nice solution. I hope after the gigafactory comes on line they dedicate a corner to make 12v replacements someday. Maybe at some point they can make them with recovered cells from larger packs and toss a custom controller in there to make a drop in friendly 12v that would work in any car. If they even got it to the same price as Lead Acid it'd be a major improvement. If they could get it down to half again more expensive than a AGM Lead acid I'd buy one for every car I drive regularly.
I'd like to see one around 20ah with pencil posts for the Prius and one around 25ah to 30ah with standard sae posts for general US car use.
But I'm not holding my breath. Apparently most of those cells are put to more valuable use in larger packs for the main pack in an EV or for powerwall type battery backup/load shifting uses. Until those markets are saturated the first run cells won't be cheap and the harvested cells will take years to trickle in.