Having leashes in the river has been debated since boards made their way into the Rockies – a well deserved debate that has driven manufacturers in the whitewater SUP niche to build safe and user friendly options. The only absolute is if you decide to wear one, it never is attached to your body but rather a releasable piece attaches to your gear (like a PFD).
If you fall off, you can use the leash to pull the board toward you and climb back on. But the leash also has the potential to drag you along with the board. However, the other option is swimming down rapids, chasing the board in that cold environment. If you decide on a leash after weighing the risk vs reward, the Badfish Re-Leash system could be your go-to.