Ad blocker

Does Avast offer any ad blocking capabilty?

As far as I’m aware not specifically an AD Blocker.
You also don’t specify what browser you are using ?

But the Web Shield though not specifically designed for that some ad- sites could well be blocked as suspect sites.

There are many Ad Blocking Apps out there depending on your browser. I use Firefox and my primary add-ons are uBlock Origin Lite and uMatrix.