It all depends on the type of memory used. DMCs are older technology that used volatile SRAM to store field adjustable parameters. Volatile means that the memory is lost when power is removed, hence the battery to keep power to the SRAM when the CPU has no power.
Tac20 is a bit newer and has FLASH memory, non-volatile RAM, & volatile RAM. The parameters are not stored in volatile RAM. The battery on a TAC20 is mostly used to keep power to the processor and clock chips to shut down safely on power loss or shutdown, & for loading software. Tac20s will work just fine without the battery installed, you’ll just have a constant 1078 fault and things that are supposed to “latch” on power loss like fire service status will not. Same goes for fault conditions that require a manual reset to clear like an SFR on a Tac32.
In my experience, the problem with replacing the battery on a Tac20 with power on is the CPU locks up and drops the WD. This is when, I suspect, parameters are lost in some cases.