No, actually it will not.The vast majority of people using Google do not care whether their data search data is being recorded or not. Heck, most even do not know how Google search engine works from 'behind' let alone worry about the difference between Google and DDG.

So they will really need something more compelling to get the average Joe (who make up the vast majority mentioned earlier), who always get his results from Google's first page, to switch from Google to DDG.

Yet, in the context of search engines, I don't see anything that could be more compelling than always getting the most relevant search results.