if you do wrap membrane around, be sure that it extends below the floor, wrapping the outside of the osb and your foundation. More than 2 inches would be ideal, even if that means digging down a little.

Again though, the lack of membrane might not impact your shed's lifespan much, just that it's "supposed to be done" due to water splashing and wicking up. Your choice of exterior sheathing looks like splashing wouldn't be an issue anyway.