Yes! Quantity Syncing must be turned on on both your Point of Sale and eCommerce in order for SKU IQ to work.
The point of SKU IQ is to sync your inventory quantities between your Point of Sale and your eCommerce platforms. If Inventory Quantity Syncing is not turned on - on both the Point of Sale and eCommerce sides - the application will not work.
There may be items that you do not want to have syncing enabled for. In order to disallow syncing for those items, you will simply not form the linking relationship described in this article on how to sync your inventory for those products.
If you've accidentally linked a product that you don't want to have the quantities sync on, contact support for assistance on breaking that link.