Kate O'Donovan from the Google AdWords team in Dublin confirmed that the mobile friendly algorithm that began rolling out last week has not impact on your AdWords quality score.
Kate actually posted the announcement about the organic mobile friendly algorithm in the Google AdWords Help forum and ended the announcement by clearly stating this algorithmic change has no impact on your AdWords ads.
Kate wrote:
Remember this update will not affect your AdWords performance or your individual Quality Scores.
Just so you have it from the horses mouth...
I should add, Google has been spotted testing the mobile friendly label on AdWords ads.
Forum discussion at Google AdWords Help.