Air carrier First Officer reported a temporary loss of aircraft control in an severe updraft that resulted in an autopilot disconnect.

Narrative

During climb after departure; the aircraft encountered moderate turbulence with a severe updraft. Vertical speed momentarily increased to approximately 9;000 feet per minute. During the turbulence encounter; the autopilot disconnected and displayed an AUTOPILOT FAIL" message; after which the system was no longer available. As a result of the updraft and turbulence; airspeed reached 253 knots and triggered an overspeed indication for approximately five seconds. Flight crew immediately transitioned to manual control; corrected airspeed; and stabilized the aircraft. No injuries occurred and the flight continued safely.Cause: The event was driven by moderate turbulence in the departure environment; including a strong vertical updraft; which resulted in a rapid increase in vertical speed and airspeed. The presence of a 240-knot departure speed restriction limited the ability to proactively adjust airspeed prior to entering the turbulence and gave us a thin margin for those types of gains and losses of airspeed . The turbulence encounter led to autopilot disengagement and a brief overspeed indication.Suggestion: When moderate or greater turbulence is anticipated or reported in the departure environment; I will request deviation from the 240-knot departure speed restriction to enable appropriate airspeed selection and improve aircraft handling margins during climb."