Can a BSOD Switch console charge?

Have a Switch console here that has a blue screen no matter what I do, tried a hard reset, tried connecting to a PC to use RCM and diagnose it that way, it just won't do anything other than show me a nice blue screen.

My question is, will the console charge in this state? My thinking is that it needs to be able to boot to get to the point where it can enable charging but right now, it just isn't at all. I only get the blue screen when its plugged in, when I unplug it the console dies.

I've checked the internal battery and it's completely dead. While connected to USB it does show 4.16v getting to the battery, I've not checked the current though.

Basically it seems like it is charging but the battery being totally flat has now died. I'm not sure if it's really worth replacing the battery as it has a blue screen, but maybe the blue screen is a result of the dead battery?

USB port and the charge related ICs seem to be behaving normally.

I should add none of the ingress indicators have activated.