In short, yes, if you listen to music on enhanced bass setups, you are changing the initial work of the artist.
An audio track goes through several processes (mixing, mastering...) before being released and these processes are supposed to "parameter" the song as the artist wants people to hear it.
Of course, it is very rare to have a sound system that has a perfectly flat response from 20 Hz to 20 kHz so in any case you will slightly modify the spectrum. The point is to modify as less as possible if you want to stick with the artist's work.
Now in your case, on headphones, I think you are referring to the Psychoacoustic Bass Enhancement technology. Since it's hard on headphones to reproduce low frequencies, companies use this phenomenon. For example, it is hard on headphones to generate 25 Hz, but if you generate harmonics (i.e. multiples of 25 Hz) at 50, 75, 100... Hz, and then remove the 25Hz, your brain will still have the feeling to hear the 25Hz.
So you add frequencies, you modify the original track. But this is your personal taste... some people prefer listening to unaltered music.
If you really need to enhance bass frequencies to hear them properly, you should also check if you don't have lost frequencies in your audition. I don't know your listening habits, but people that very often listen to music with headphones tend to higher the volume in time. If someone around you at one meter distance can also hear it, it is a sign that the volume is probably too loud. Then it becomes a viscous circle, "I have a little hear loss, so I increase the volume, so I damage my hear a little more, so I increase the volume etc...". Hear loss doesn't suddenly hurt, it is a small, long term process and when you realize it, it's sometimes too late.