While running BraiinsOS from SD card on an S9, can the spare storage space on the SD card (in the case where the card storage space is larger than the OS firmware) be accessed, eg from a custom modification of the BraiinsOS?
No. But if you can get a 32gb card to work (some do) and if you partition it into a 16gb and a 16gb . you could access the empty one with proper programming.
The control board is pretty much a cheap small pc/rasp pi/beaglebone
so a proper os done exactly correct could access the second empty partition.
I can't imagine why you would do it. care to tell us your idea?