After linking already listed Etsy products with their respective Shopify products, the Etsy variants get overwritten by Shopify ones. It means the product's information on Shopify will be overridden on Etsy.
Example: I have 5 variations on Etsy products name ABC and the same product listed on Shopify as Simple products with no variants.
If you link this product from the App then Shopify product will override on Etsy product i.e it makes that product as Simple on Etsy too!