Can squarespace e-commerce record and track serial numbers with a Square pos/card reader?

This scuba dive shop has over 300 scuba diving products in their brick and mortar store. They need a way to do online sales, as well as in person sales in the store.

The dive shop has to use a system that records individual serial numbers for each individual product item--not just the sku for the product.

Is this possible? What would the process look like of scanning in the products in-store with a barcode using the Square reader? 

Thank you!