Connect a decent-quality DAC (like one of those listed above) to your laptop or phone or other digital music source, and you should hear a sonic improvement in the music you're playing through it, whether it's from Spotify or Tidal or locally stored files. However, a DAC can only deal with (convert) the quality of the digital file/stream it is handed, and Spotify's maximum bitrate of 320kbps is rather limited compared to high-resolution streams from many rival services.
So yes, you should hear a positive difference during Spotify playback if you add a good DAC to the equation – so long as (and this is important) your headphones or speakers are transparent enough to communicate what the DAC is doing.