yes, certainly, as mentioned mac addresses are an obvious one, usually in a flash/eeprom next to the mac if it is a separate part, or in a flash/eeprom elsewhere. vital product data (board serial number, etc) can be placed in a separate eeprom or flash or in the same device used to store other firmware.
When you have a situation for example where field upgrades of the firmware are possible, part of the system design, you dont want the VPD data erased when the firmware flash is erased and reprogrammed, so you need to solve that by either using write protect features of the flash device (putting the VPD in its on bank/area and locking that area), and not necessarily publishing/documenting publicly how to release the write protect pin and/or some other solution such that you can program the VPD in mfg and then keep it locked otherwise (a pull down/up as required then when programmed during/around ICT that fixture can pull it the other way).
It is probably more common than you think, medical is but a very very tiny subset of folks that would do this. Maybe not a television remote control but probably a mouse or keyboard and certainly a cell phone, etc.
If/when a sticker is also used on the board, you may find it has a barcode, so that during manufacturing the fixture or operator can scan the barcode, assembly rev, etc and add that to the VPD for that board.