What it will do is open the connection to the speakers (or output amplifier, depending upon how the jack is inserted into the circuitry) and the barrell of the plug will short the output of the left and right channels together. As mentioned, there is likely enough source resistance that there will be no ill effects. If you can set your stereo to monophonic operation with mono headphone operation, you'll definitely lower the chances of problems as both channels will be carrying the same program material.