Where I live, the only code rules that apply are that the AC power and low-voltage data cables must not be in the same conduit or wall box. Other than that, it's generally a bad idea to add extension cords.
A cheaper way to do this would be to route your data cables through the wall, and use 1 or 2-gang boxes top and bottom to "terminate" the cables, and use a simple oven outlet cover plate at each box for a tidy look.
For the power, if you want to add an outlet behind the screen, you can do the same thing but will want to ensure the 14-2 or whatever you use is apart from the data cables, and also terminate the wires in a box. While it's best to mount a new box for the power to a stud, you can use a "remodel box" as well between studs. Any AC wiring junctions/splices need to be in a box and accessible, no hiding wire splices in the wall.