Depends on what you call a driver.
If you mean some software that should be loaded at DOS startup for the card to function - then no, it is not needed.
But anyway any software meant to interact with Adlib or Sound Blaster must include some piece of code that knows how to do it properly. This piece of code can be (and usually is) called a driver.
There might be some situations when more than one driver is involved. For example, let's say we're running Warcraft II on a Media Vision Pro Audio Spectrum. This way, we have two drivers between the game itself and the sound card: low-level driver MVSOUND.SYS which is loaded via CONFIG.SYS during DOS startup process, and middle-level drivers PROAUDIO.DIG (for digitized sound) and PAS.MDI (for MIDI music) that are loaded during the game startup. These middleware drivers are interacting with MVSOUND.SYS instead of the soundcard itself.
Hardware comparisons and game system requirements: https://technical.city