Yes.
Some say the Program Settings, Update (Basic), Details button, Running Mode Silent works (see image1), some don't, try it and report.
Or Program Settings, Sounds, Settings button, from the pop-up scroll down to find the avast! Antivirus, Automatic VPS Update and select a different sound .wav file by clicking the Browse button. Many select either the ding or tada in the Media folder, you can browse around and select any you like, see image2.
You could however choose the nuclear option and Program Settings, Sounds, enable Disable avast! sounds, everything.