Yes, you must have access to edit the HTML source code of the website you submit in your application in order to be able to display Google ads or an AdSense for search box.
If you’ve created a website via a content management system (CMS) providing hosting (for example, Blogger, WordPress), you can submit its URL providing that you have access to AdSense or to the HTML source code from the interface.
Create a new blog using Google’s weblog service, Blogger. Through Blogger, beginner webmasters can display Google ads without ever copying or pasting HTML code. Signing up for a Blogger account is fast, easy and free.
Once you’ve created your blog, you can begin displaying Google ads in minutes by following the instructions here.
Create a new site using Google’s web hosting service, Google Sites. To begin designing and publishing your own Google-hosted website, please visit http://sites.google.com. For more information, read “Adding AdSense to your Google Site”.
If you submit a site you don’t own (for example, http://www.google.com), you won’t be able to place the AdSense code on the site and your application will not be approved.