Does a creature returned by the Undying effect have summoning sickness?
Yes,

A creature with undying returned to the battlefield would have summoning sickness.  Undying does not provide an exception to the general rule.


  302.6. A creature's activated ability with the tap symbol or the untap symbol in its activation cost can't be activated unless the creature has been under its controller's control continuously since his or her most recent turn began. A creature can't attack unless it has been under its controller's control continuously since his or her most recent turn began. This rule is informally called the "summoning sickness" rule.


As you noted, the Undying creature returns as a new creature and thus has not been under its controller's control continuously since the the turn began.