I'm just taking a guess, but I don't think its factory either. My BoP board was 3 double A (and your first pic looks like it was as well) and the soldering definitely looks like someone soldered that battery in there. I personally did the solderless remote battery from Marco and love how simple it was to put in.

The solderless remote adapter from Marco requires you to have a 3 battery holder on the board. So in this case, it would still require soldering. NVRAM kits are considered the best option on the market (that I know of) and at this point it would probably be best to go this route.

I personally don't know how long this battery would take to discharge, I am sure someone else on the forums will be able to answer that question for you though.