I think so, yes.
A rejected promise is equivalent to a node that throws an error. Flyde exposes a default "error" output pin for each node. As everything in Flyde is async, any error thrown can be viewed as a rejected promise.
Promise.any can be achieved with 3 promises and a throttle node
Promise.allSettled translated to connecting the error output pin and hooking it to whatever you wanted the fulfilled value to go.