ASA has a specific rule citation (8-7X) saying runners put out when batter is discovered using an illegal bat, if appealed before the next pitch, stay out. The equivalent ISF section (8-9, The Runner is out when
does not have this same rule, and it isn't stated in any reference to using an illegal bat that anyone other than the batter is out.
I would say batter is out, and runners return to the last base legally touched at the time of the pitch.