I would not expect the conformal coat to cause a problem.
If multiple (all?) boards are having the same apparent undervoltage, I'm sure you have checked the obvious cell count configuraiton.
The IC is sensitive to the absolute maximum differential voltage. A common damage is a resistive short between 2 inputs. This can reduce the voltage measrued on the cell and raise that of the adjacent cells. The leakage may be measurable with an ohm meter (use one which won't force excessive voltage). On the board which shorted the cell- to soldering iron ground, if the iron tip touched the pad before the cell terminal, it would most likely have damaged one of the differential inputs. A resistive short between the inputs would discharge one cell with time and show as a battery voltage drop. The IC would seem to be in shutdown mode from your description and should be in a low current power state, so some resistive leakage would seem the likely cause..
Programming is typically not affected by an input short, so success of programming does not indicate the part is damage free.
If your conformal coat leaves the programming interface and VOUT available, you might put the part in host mode and look at the voltage of the cells. If one cell shows a higher VOUT (lower cell votlage), it is the likely damaged input pair. If a pattern shows up on the damaged boards, it may indicate where to look in the board assembly or test process for unexpected voltage levels.
Zener diodes at the board input either in the assembly fixture or as part of the product could help prevent overvoltage and damage.