Disabling a category will not hide products in that category from the search.
When you disable a category, then Magento will not show that category in main menu, layered navigation etc. In short, Magento will not use that category in any of category related operations. That means, if you need to access that category, you need to explicitly specify it.
Categories and products are two different entities. So when you disable a category, it will not hide its related products. This is because products have self existence. So as we can disable a category, we can disable a product too.
Just open an existing product through admin. You can see a field that is used to set
visibility. There are multiple options there. Most probably in your case, it is set with
catalog & search. It means, this product would be available for all catalog related operations and during search. If you do not want to show that product from search, you need to change this option wisely
Hope that makes sense