Hi Banzai77, welcome to the forum
Yep, there is a way...
Right click avast! tray icon --> program settings --> 'update (basic)' tab --> details --> Uncheck 'show sliding box after automatic update'
I am not sure if this disables the voice section of it though.
What you can do, if the sound is still there:
program settings --> 'sounds' tab --> click settings --> scroll to avast! antivirus --> change the sound for 'automatic VPS update to none in the drop down box.
-Scott-