ALSO - romex IS NOT designed to be used in any type of conduit due to heat
Plugs are NOT allowed to be installed onto solid conductors ! They may break over time
Both ends of solid core wires and the cable itself must be fixed in position - as in the wall - not moveable
Might I suggest a slight modification that will actually sound better
1. Go to Home Depot and buy the single conductor stranded wire that electricians use inside conduit - get White, Black and green
2. Take the three wires and braid them (tighter the braid the better).
3. Insert them into the conduit for safety
Attach the box and plug as planned
The braided cable will result in a lower noise floor.
I think this method may up to code because the wires are stranded and the wires are protected by the conduit
But I would check your local codes first
Regards