It depends on the DAC in your PC and the quality of the data stream. For free Spotify (160kbps) it's likely the onboard DAC is adequate. For the high quality streaming option (320kbps) you will probably hear a difference. IME most onboard computer DAC's leave a lot to be desired sound quality wise. When fed a signal of sufficient quality an external DAC will usually outperform any built in DAC.
I stream music from the web via Spotify and various web radio stations. I use them mostly for discovering new source material. For serious listening I prefer the FLAC files I've ripped from my CD collection. All music sourced via my music server PC, streamed or stored on HDD goes through an external DAC.