Yes and no. There’s no “BIOS” at all, so definitely no BIOS update. I assume you mean firmware updates for various hardware components.
Yes, there are some firmware updates but whether you should install them depends on whether you need them i.e. whether you are encountering any problems that are relevant. I would say that a phone switched off in a drawer encounters no problems 
so I would ignore any possible firmware updates at this stage.
FWIW, by reflashing the phone, you will automatically update uboot. So that’s at least one additional update taken care of.
The firmware you are most likely to need is updated mobile modem firmware but that depends on what country you are in i.e. its progress in adopting VoLTE and switching off the 3G network - and also depends on whether you will use suspend (which you probably will).
Otherwise: Manual Updates for Librem5