Hi,
The answer is yes and no
You can't use the id of the menu item with the name "kolekcje" because when you access that page, it doesn't display any products and you don't want the categories to appear on the search results page.
However, what you can do is to create a new menu item of the type "products listing" configured to display all your products (set the "main category" to your main category, and set the "sub elements filter" to "all sub elements"). And then you can use the id of that menu item in the "menu" setting of the module and it will display your search based on all the products on the shop.
Also, if you turn off the "force redirect" setting of the module, it will use the products listing of the current page for the searching and only redirect to the menu item of the "menu" setting if you use the filter module on a page which is not a products / categories listing.