That's a good question for headphones, as you won't get the same superposition / interference patterns that you get with loudspeakers in sound field or free field.
There's the question of absolute phase and relative phase, too. Relative phase refers to one ear's monitor being in phase (homophasic) or out of phase (antiphasic) with opposite ear's earpiece. In a sound field, anti-phase, = 180 degrees out of phase, results in cancellation of low frequencies (destructive interference). In the case of earphones, the perceived consequences to music aren't as well documented. There's literature in audiometry alluding to speech signals under antiphasic earphones. The effect is very real, so you at least want the relative phase of earphones to match.
You won't damage your headphones or your hearing based on phase "correctness". It is often difficult to ascertain the absolute phase of a signal because you have to know the whole audio chain (inverting and non-inverting gain stages). For example, does the compression from a kick drum result in compression wave from earphone, or does the earphone membrane move in concert (absolute phase) with original source signal?
At very least, you do want the earphones to work in concert so the L and R are matched in relative phase. Unless you have separate L and R connections (i.e., no common ground connect between earphones), the headphones should always be matched to one another... unless manufacturer made a boo-boo.
Best,
CochlearConcept