FWIW, I have a Debian derivative called Knoppix installed on FAT formated flash, the persistent home directory is called "knoppix-data-img" and was in the Knoppix folder. I mounted it in Debian with command: mount -oloop knoppix-data-img /test
, the test directory I created many moons ago and already existed, and I was able to access the data within. So this should not be an issue with Mac also, in Windows you would probably need third party software to mount and image.
has a quick and easy method, not sure if it formats FAT, but this is where I went to put together my Knoppix.