Hi,
Yes and not. You can enable the HikaShop wishlist module. And that way, when you add a product to the wishlist, it will appear in the wishlist module, similarily to what's happening with the cart module when you add a product to the cart.
However, there is no information directly on the product itself that it has been added to the wishlist.
Note that alternatively to the wishlist system, we also propose this "like" plugin:
www.hikashop.com/marketplace/product/155-product-like-btn.html
This might be what you're looking for instead of the wishlist system.