When speaking of a logic AND or other gate component, these are standardized to either TTL logic (old fashioned, more power hungry), or modern CMOS logic standard voltages, CMOS being the full 5v rails of the power supply for them (you do need a standard logic chip power supply to use them, whatever the input voltages...). You won't get that out of the voltages on the balancing current resistors in the balancer I suspect, though I am not completely sure how those work. What you usually would have to do in order to perform logic operations on non-logic part voltages is use voltage comparators which effectively do parts of the logic on arbitrary voltages, by converting the arbitrary inputs into pure logic level outputs -- takes a lot of parts in some cases, depending on how complex a relation you want. It would seem to be simpler just to use a comparator to detect the maximum charging voltage on the battery instead of differentials across cells used by the balancer controller IC.
The original German balancer is analyzed at the beginning of this thread, using an individual cell circuit with a simple comparator no longer made, LBA1. This balancer was made to be stackable, with a separate small board on each cell in any size pack. The lithium batteries using this for the XV models were made by member Hausman of Roboter-Forum.com, thread Lithium Ionen Upgrade https://www.roboter-forum.com/index.php?thread/5804-neato-lithium-ionen-upgrade/
A custom board was made when the original comparator ceased to be made.
Technically the controller IC for balancers monitors differentials between the cells and not the overall battery voltage. Balancing current presumably flows at any time, not just when the battery is full, as it tries to keep the voltages on all the cells equal at all times, I think. Balancers incidentally, seem to be mostly used in external battery chargers, instead of inside battery packs. There can be separate pack balancing cycles performed after main battery charging cycles, is my impression -- more expertise needed.
I once posted on the German forum some idea of supplementing the balancer with a direct voltage to temperature signal. There may have been a way to do this with the old LBA1 version but I would have to check, and it probably would not work on the newer, controller IC types. Maybe you would know this engineering better -- I'm just self-taught hobbyist.
Incidentally the LiFePo4 cells are described as "self-balancing" requiring less of the balancing circuits used with lithium polymer to extend the life of battery packs with varied aging of the cells.
The common protection boards, for both over and under voltage (excess discharge as with short circuits), are to protect the battery from failures in the attached electronics including charging and discharging. These are more critical with lithium ion than LiFePo4 because of a fire hazard with the former, besides damage to the cells. If such failures in the Neato system board are considered unlikely, there is less need with LiFePo4. Neato has protection against over-discharge in software in that it shuts down when voltage is too low to run the system, besides normally keeping around 30 per cent charge unused as a buffer against damaging deep discharge, and reserve for returning to base.
Incidentally the German guys were professional engineers who just played with the Neato as entertainment.