ThujanWhat model? I ask because plugging headphones into the back of the computer makes things awkward.
The sound card is better than using the audio port on the front of your machine. As long as there's no interference I don't see any problems.
You could always benefit from an external source but, you already invested in buying that soundcard so it's up to you to spend more for a "better" experience.
ThujanI'll share my experience.
Used headphones out of laptop for a long time without thinking of the sound quality.
Purchased an external sound card (Asus Xonar U7) and noticed cleaner sound.
Built a computer with a motherboard that had 'claimed' better audio internals and a more powerful amp but found out that it was pushing too much power to my headphones and would hear static noises at really high levels.
Bought an external DAC/amp (in my case SMSL M8/V2 amp) and the sound quality is the cleanest it could be.
Edit: Safest bet is to decide whether or not you need one after you listen to your headphones and make the judgement yourself.
ThujanIn my experience it DEFINITELY made a difference to get a good external DAC and amp. I ended up going with the Schiit Modi Uber for DAC and the Bravo Audio Ocean for a headphone amp--twice as much as what you're looking for, but there are some great small combo units out there from Fiio and others. Like has been said, try something out in store, or at home if you can return it.