With Teslas, the load on the 12v system is minimal to say the least. The voltage will typically fall below the warning level far before it becomes low enough to actually impede the functionality of the Tesla minimal 12 volt system. There are very rare instances of instant battery failure but this is atypical and generally the result of some sort of manufacturer defect or physical damage. The eventual demise of lead acid cells is much more predictable in almost every instance. This is why you typically have months when the car warns you before you actually have to replace the battery.
This is part of what makes overpaying for a "high performance" lithium ion 12v battery the definition of pointless. Pure marketing & the lemmings who fall for it make the economy strong I guess. Like your blinkers are going to blink better in a Tesla or something. Lulz I digress.
Your delayed boot up has nothing to do with your 12v system. It's more acute than that & is likely your MCU for various reasons. The MCU2 isn't as big of a step forward in terms of hardware as some would believe. Newer software will continue a gradual March to the same performance as MCU1. Until they make optimizing firmware a priority this planned obsolescence will continue. Their focus is on adding features like farts, fireplaces & outdated video games though so it's not likely we'll see any resources wasted on something "useless" like optimization for legacy hardware compatibility.
While you're at it, check the installed price to compare. Last I heard it wasn't much more to just have them come wherever you are to put in a new 12v battery and then you don't even need to worry about it. You also don't have to avoid messing something up (someone recently posted that they connected the wrong connectors to the wrong +/- on the battery... yikes!) and don't have to be in the heat or cold. Some things are just worth a few bucks and that is coming from a guy who historically was ALWAYS his own mechanic. Tesla has a few things that are reasonably priced and I would take advantage of those things whenever possible.