When the search override feature is not active, then the search results page will display the default WooCommerce search results. Once you activate it, the plugin will try to force the same results there.
The most likely reason it started working after that modification is, that without the override the WooCommerce query is modified with the SKU search, and registers the change. Generally it should work without that code if the override is active.
If there are still any issues, then you can add temporary back-end and FTP access and I will take a closer look.