First of all, you need good SPEAKERS or HEADPHONES to see a big difference.
As for audio, there are TWO main reasons for good sound:
1) the digital processing, and
2) the amplifier/noise isolation
When you use a DAC that means you send out the DIGITAL audio. If it's a USB DAC there's a small overhead because the CPU is doing the processing. 5% on my i7-3770K?
If it's not a USB DAC it may have a TOSLINK connector, so you'd still use the ALC892 for example. Less CPU overhead but the ALC892 isn't as good as the better DAC's.
*I have the ALC892 and can tell you a good SOUND CARD or good EXTERNAL DAC solution are noticeably better with good speakers. Especially for:
a) noise separation, and
b) bass
It's hard to describe but it's a big difference. My sound card would be similar to a modern $100 to $200 card. Asus, Creative etc.
I've also used a good USB DAC which is built into my speakers. Audioengine HD3 (expensive).
My speakers are relatively small due to limited desk space. The best computer speakers (ignoring surround which is a hassle), are
a) 2.1 (stereo + subwoofer), and
b) 2.0 (stereo) ... *without a subwoofer it's best to get at least 4" woofers if you can afford the desk space.
THESE look similar to speakers I had before which had great sound:
https://www.amazon.com/Pioneer-DJ-DM-40-PAIR-Excellent/dp/B01DW36BO0/ref=sr_1_4?s=car&ie=UTF8&qid=1506289160&sr=8-4&keywords=desktop+pioneer
(you want speakers with their own amplifier, not bookshelf speakers that need an amp)
Do you need desktop speakers?
You should also consider the CONNECTORS you need. If you use a sound card, can you drive both the desktop speakers and the headphones? (I can do both, but I just plug my headphones into the desktop speakers)