When you hire Yelp Delete to disappear from Yelp - that is exactly what happens.
Let's assume your business is "ABC Lawyers" based in Miami, FL.
After hiring Yelp Delete to disappear from Yelp - no one will be able to find the Yelp page for "ABC Lawyers" in Google or Yelp search results, even by searching directly for your business.
Yes - even if you went directly to Yelp and searched for "ABC Lawyers" in Miami, FL - your business profile would not show up.
Yes - even if you made a Google search for "ABC Lawyers Miami FL Yelp Page" - your business profile would not show up.