I shall try to find the relavent circuit but it is unlikely that the headphone circuit would be damaged by the use of a TS plug though of course you would only get the left channel. This is because historically, headphone amps had a physical resistor of between 22 and 80 Ohms in each output circuit. The resistors performed several useful functions. They tended to equalize the power into headphones of various impednace. They kept the amps stable even on very long lines and, most importantly, they protected the ampliiers from shorts.
About a decade ago there started a fashion for headphone amplifiers have a very low, often nominally zero, output resistance. I am not sure how "bombproof" such circuits are, especially at the budget end of the market?
Dave.