Yes, you can add a new variant to an existing product that is already published on your Squarespace store.
Add the new Variant in Squarespace
Firstly, create the new variant manually in Squarespace. You can do this by going to Commerce > Inventory
Click on the selected product
Click on Manage option in the top right corner and Add option
Provide the name of the new variant and click on Save.
The steps might differ, depending on whether you are using Squarespace's new or classic product editor.
You can read more about this in Squarespace's Help Center article Adding product variants.
Sync products in Gelato
Once the new variation is created in Squarespace, navigate to the Stores section and select your Squarespace store. Click on the "Sync products" button is located on the top right of the page. 
After a while, you will see a new variant as "Not connected".
Connect the new variation in Gelato
You will now be able to connect the new variation to a product in Gelato as shown here.
Note: If you need to add many variants, it might be faster to create the product from scratch following the steps described here.
