Do I still need to add verifications if the site has been verified through Google Analytics?
It's up to you, of course. from the module's page:


  This module is useful for the following search engine verifications:
  
  
  Google Webmaster Tools
  Google Apps
  Bing Webmaster Central (formerly Live Search)
  Yahoo! Site Explorer
  Yandex.ru
  Any search engine or web service that uses META tags or file upload to verify that you are the owner of a site.
  


You are the one to know if you will need or want assistance with verification against above tools.