Since everyone joining is screened for a Secret clearance I don’t see how any of them would be eligible. But then again Bath House Barry couldn’t get a clearance either as his background is hidden.
Back when it used to matter, and the rules were followed, over half of Clinton's White House staff could not even get a Confidential security clearance, much less Secret or Top Secret - so tainted were their backgrounds and sins.
Obama's crew may be tried for treason some day.