Can I wire a receptacle to a cord and plug?
Use an inlet (or a full in-wall TV power kit, if required by the AHJ)

What you want for getting power back into the wall isn't a second outlet, but its mirror image, namely an inlet (product shown for exposition only):



That way, you can use a (short) length of ordinary extension cord between the surge protector and the inlet, then have normal building wiring from the inlet to another outlet.  This is similar to a 400.7 (11) setup:


  (11) Between an existing receptacle outlet and an inlet, where the inlet provides power to an additional single receptacle outlet.  The wiring interconnecting the inlet to the single receptacle outlet shall be a Chapter 3 wiring method.  The inlet, receptacle outlet, and Chapter 3 wiring method, including the flexible cord and fittings, shall be a listed assembly specific for this application.


only with the surge suppressor in the middle, which to me, would make it fall under 400.7 point 6 instead (you're facilitating the interchange of the surge suppressor or other intermediate device here).  However, your AHJ may require a 400.7 (11) kit -- these are called "in-wall TV power kits" generically, but are sometimes known by a trade name of "PowerBridge".  These include the inlet, outlet, and the wiring between them in the wall, and typically are designed to be easily field fitted, using an integral connector system.