Reddit user brokenwiener reported that the new beta version of Steam has the ability to enable sounds when receiving in-game rewards:
Apparently, Steam has an Achievement Sound in Beta right now, and Achievement Tracking.
by u/brokenwiener in Steam
If desired, the sound accompaniment of notifications in the desktop client can be turned off. However, there is no separate switch for achievements in beta yet, so you can only mute all non-critical notifications at the same time.
It is not yet known when Valve will port this feature to the stable version of the launcher, or if they will do so at all.
Source: reddit