Yes and no. In both the Free and Premium versions of Spotify, you have the option of choosing the quality. However, with Spotify Free, your “High” option caps out at 160kbit/s, but if you’re a Premium subscriber, you can go to “Very High” which will stream at 320kbit/s.
Also, by default, Premium will play in your web player at 256kbit/s, while Free will play at 128kbit/s. So depending on your hardware and preferences, Spotify Free’s “High” might be good enough for your needs.