No - When you mark a Yelp location as closed, it won't completely disappear.
Users who specifically search for your business by name will still see your Yelp page in the search results. The only difference is it will say "Closed" beside it, which will cause a decrease in customers for your business.
Note: Marking your Yelp page as 'closed' can actually make it harder to make your Yelp page completely disappear.