It is not a question of whether this will work, but rather that this is not a wise idea. Basically, ordinary flash drives are not designed to withstand the amount of reads and writes that an operating system will require. Certain versions of linux provide a solution referred to a persistence. This is where the operation system creates a temporary drive in volatile RAM which can used be for read and writing. When you shutdown the operating system, the contents of this RAM drive is written to the flash drive. When you restart the operating system, the saved data is read from the flash drive into a new RAM drive.
To be clear, most of the operating system is considered read only and resides on the flash drive. Only the files that may may change often reside on the RAM drive.
There are many utilities that can create a flash drive version of linux with persistence. However, the few I have tried would not boot on a Mac.