I have a hard time envisioning the physics that link a SSW to a subsequent el nino (or la nina). I imagine the top-down effects would be confined mainly to the polar domain or mid latitudes, but not tropics. Conversely, enso is driven mainly by tropical ocean-atmosphere (KWs and WWBs mostly) and then those forcing effects propagate to mid- and polar-latitudes via rossby waves, and then bottom-up into the stratosphere. But the other way around? I dunno.