Yes, you can add the SKU to each variable product as shown in your screenshot.
How else can I include the variable sku’s in the search?
To include variable SKU’s in the search, you may need to use a third-party plugin like Advanced Woo Search to enhance the default search. Please feel free to try it out and let us know how it goes.
For variable products you can keep the inventory tab clean and manage the stock, SKUs and all the inventory details for the individual variations. Yes, WooCommerce will know to look for each individual variable for their SKUs!