I would hate to see Jeffries here, but I really don't think we have to worry about him.
With his last 2 appointments Boyle has shown he has been looking for a younger manager, with a good reputation, who wants to develop a philosophy of good attacking, passing football at the club. He seems to be looking for them to also place an emphasis towards giving the youth players their chance in the first team a bit earlier than other teams/managers might do.
For me Jeffries doesn't suit either of these categories, and with just about all of his old Hearts team retired he's running out of options for signings to make.