Usually if anything plugs into the mic jack it will cut off the internal camera mic even if no sound is coming through the plugin mic. What I would do to test it is record video with out the external mic and tap/rub the camera mic that is located directly above the EOS 5D emblem. In this video you will hear loud noises as your finger interrupts the mic. Do the same thing again in another video but with the external mic plugged in. If the external mic is plugged in and you tap the camera mic just above the EOS 5D emblem and hear little/no interference, then the external mic is working and active. How cheap was the mic? You honestly may not notice too much difference on a super cheap mic. It also depends on what your shooting.
2x 5D mkiii, 7D, 60D, T2i, Tokina 11-16mm f/2.8, Bower 14mm f/2.8, Canon 15mm f/2.8 Fisheye, 24mm L f/1.4 ii, Sigma 35mm ART f/1.4, 24-105mm L f/4.0 IS, 50mm f/1.8 ii, 85mm L f/1.2 ii, 100mm L Macro f/2.8 IS, 135mm L f2.0 75-300mm f/4-5.6, 70-200mm L f/2.8, Sigma 70-200mm OS f/2.8. StockhamMedia.com