After updating avast through the GUI will it affect anything if instead of clicking yes to restart, I click no and shut down?
No.
The reason the answer is “no” is that by shutting down your machine and by re-starting it again
you accomplish the same thing…reboot.
Also just to mention, there are some that are finding it may take an extra Re-boot OR 2.
It can sometime take an extra Reboot to get everything (Drivers etc.) registered and settled in. 