Well, do they? No.
Google defines Quality Score as “an estimate of how relevant your ads, keywords, and landing page are to a person seeing your ad. Having a high Quality Score means that our [Google’s] systems think your ad, keyword, and landing page are all relevant and useful to someone looking at your ad.”
Google Adwords’ new enhanced campaigns will not bring about the change to the way QS (Quality Score) is currently determined. You can also rest assure that once you update your current (what Google is coining now as legacy) campaigns to the new enhanced version, you will not lose any of the historical QS information as long as your ads, keywords, display URL’s, and destination URLs stay the same.
Here are two example scenarios to help give you a better understanding when you begin to upgrade your device specific campaigns.
Example Scenario 1: You have Desktop Only campaigns for your products, and now want to upgrade your B2B Desktop Only campaigns to the new enhanced version.
Because you simply upgraded it without making any changes to the ads, keywords, destination URLs, etc., the QS (Quality Scores) historically attached will stay the same within the desktop devices. Your keywords will now just begin to get separate mobile QS ratings based on their specific performance moving forward on those devices now that the campaigns target all devices in the single campaign level.
Example Scenario 2: You have a Desktop Only (Campaign A) and a Mobile Only (Campaign B) campaign for your products. Each of these campaigns contain different ad copy specific to the audiences on the separate devices.
When updating Campaign A, the same logic from Example 1 above still applies in terms of QS (Quality Scores). If you want to keep the QS attached to the unique, mobile specific Campaign B, then you will need to copy these ads into the upgraded Campaign A group as mobile optimized ads. You can then pause or delete your old mobile only legacy campaigns.