No inventory information for catalog items

I’m noticing that there are a large number of catalog item variations with NO associated inventory entries. Is this possible? are merchants able to activate or deactivate inventory tracking for certain items?

Yes, you can turn off inventory tracking via the API or within the Square Dashboard. In the API, when you retrieve a catalog variation object, within the item_variation_data field, you will find a boolean called track_inventory that can either be true or false. See complete response here:

If inventory tracking for an item is turned OFF by a merchant, does that mean that when that item is sold, it will NOT create an associated inventory change? (i.e., from IN_STOCK to SOLD)

That’s correct. If inventory tracking is turned off then the inventory won’t be updated (if it was previously being tracked, it will remain at the same stock if you decide to start tracking it again). No Webhooks will be triggered.