Centering websites navigation around the search box – Good or Bad idea?

I'm working on a website for a pharmacy store. The store would feature lot's of different drugs for different illnesses.

I had and idea to make 90% of the navigation center around the search bar. Meaning the website would have a normal navigation bar with sections for specific categories, but the landing page of the site would look basically like google.com with just a navbar and a big search box in the middle with a title "what are you looking for?" and a placeholder "Drug name or illness"

The user could input the name of a specific drug to look for it in the store catalog, or write in an illness or ache they are need a cure for.

For example writing "headache" in the searchbar would give the user an array of different painkillers suitable for headaches.

I was thinking if this is a good idea, and could actually help the websites ux.