This was really true about 10/20 years ago, when common motherboards didn't fully support onboard sound cards and had to rely on dedicated PCI or ISA soundcards.
Today most integrated onboard sound cards do just fine for listening music even if you want a good sound definition, so having a good set of speakers or headphones along with the compression and format of the audio files do have more of an impact than the soundcards on your motherboard.
But if you are that kind of enthusiast that really really believes his ASUS Xonar Essence simply makes his music sound better no matter the format it is, just go ahead.
Now if you are musician and works with recording and high definition sound editing, getting a dedicated soundboard is advised.
TL;DR: Soundset (AKA: Headphones, speakers) matter more than the soundboard, unless you want to record high quality shit.