Is it safe to mount a surge protector strip behind a wall-mounted television?
Technically, this is not okay. Wiremold® and other similar products are not typically listed for use with power-supply cords, cordsets, or other similar cables.  They're designed to contain data, communications, and audio video cables. See this answer for more details.

Check the manufacturer's documentation, to determine exactly what types of cables are allowed in the specific product you're using.

As for plugging the surge strip into the extension cord, that's definitely not allowed. There should be a label on the strip, or in the documentation included with the strip that says not to plug it into another strip of extension cord.


  UL White Book 2013
  
  Relocatable Power Taps (XBYS)
  
  ...Relocatable power taps are intended to be directly connected to a permanently installed branch circuit receptacle. Relocatable power taps are not intended to be series connected (daisy chained) to other relocatable power taps or to extension cords.


The common solution to this problem, is to use a kit designed for this, like the one described in this answer. Though with a system like this, you'll have to cut holes in the wall. 



If the wire management channel is a listed raceway, then you shouldn't be running power and communications cables through it together. Unless the raceway is divided for the entire length.


  National Electrical Code 2014
  
  Chapter 8 Communications Systems
  
  Article 800 Communications Circuits
  
  800.133 Installation of Communications Wires, Cables,
  and Equipment.  
  
  (A) Separation from Other Conductors.  
  
  (1) In Raceways, Cable Trays, Boxes, Cables, Enclosures and Cable Routing Assemblies.
  
  (d) Electric Light, Power, Class 1, Non–Power-Limited
  Fire Alarm, and Medium-Power Network-Powered Broadband
  Communications Circuits in Raceways, Compartments,
  and Boxes. Communications conductors shall not be placed in
  any raceway, compartment, outlet box, junction box, or similar
  fitting with conductors of electric light, power, Class 1, non–
  power-limited fire alarm, or medium-power network-powered
  broadband communications circuits.
  
  Exception No. 1: Where all of the conductors of electric
  light, power, Class 1, non–power-limited fire alarm, and
  medium-power network-powered broadband communications
  circuits are separated from all of the conductors of communications
  circuits by a permanent barrier or listed divider.