The council shall designate from among its members a chairman and vice-chairman who shall serve for 1-year terms and who may be reelected. Membership on the council shall not constitute holding a public office, and members of the council shall not be required to take and file oaths of office before serving on the council. The council shall not have the right to exercise any portion of the sovereign power of the state. A member of the council shall not be disqualified from holding any public office or employment by reason of his appointment or membership on the council, nor shall he forfeit the office or employment, by reason of his appointment hereunder, notwithstanding the provisions of any general, special or local law, ordinance or city charter.