You can do that with and add-on such as New Tab Homepage or NewTabURL.

If you don't want an add-on, while this isn't an exact fix, it may help to know. I just tested this, and it works:

The blank page address bar can function like the Google search homepage. When you open a new tab, just start typing as you would if you had the Google search page open. The address bar is selected upon opening the new tab. When you hit ENTER, it will either bring up the usual Google results page, or it will go directly to the website that matches your input - it depends on how narrow-focus your entry is.

For instance, try typing "butterfly" and you will get the Google search results page (being a very general subject). The same if you type in "Map, San Francisco, CA."

However, If you type "Flickr", you will get the Flickr homepage (being more specific).

Note: my homepage is the Google search page - but I don't think it affects this blank page behavior - I believe it is a natural default.