Weather Resistant Outlets vs Weather Proof Box
Yes. If the receptacle is in a wet or damp location, the receptacle must be a weather-resistant type.
In a damp location, you can use any weatherproof cover.  In a wet location, you must use an &quot;extra-duty&quot; cover. &quot;Extra-duty&quot; covers, provide  weatherproofing even when a cord is attached to the receptacle.

National Electrical Code 2014
Chapter 4 Equipment for General Use.
Article 406 Receptacles, cord connectors, and attachment Plugs.
406.9 Receptacles in Damp or Wet Locations.
(A) Damp Locations ...All 15- and 20- ampere, 125- and 250-volt nonlocking receptacles shall be a listed weather-resistant type.
(B) Wet Locations.
(1) 15-and 20-Ampere Receptacles in a Wet Location. ...All 15- and 20 ampere, 125- and 250-volt nonlocking-type receptacles shall be listed weather-resistant type.
Chapter 1 General
Article 100 Definitions
Location, Damp. Locations protected from weather and not subject to saturation with water or other liquids but subject to moderate degrees of moisture.
Location, Dry. A location not normally subject to dampness or wetness. A location classified as dry may be temporarily subject to dampness or wetness, as in the case of a building under construction.
Location, Wet. Installations underground or in concrete slabs or masonry in direct contact with the earth; in locations subject to saturation with water or other liquids, such as vehicle washing areas; and in unprotected locations exposed to weather.