Hello,
 
Not directly, as it’s just an indicator on how many variations the system is able to generate based on your input.  
 
It of course can indirectly affect it, by not performing as well as it could due to not having more variety for the system to pick from.
 
Remember, QS for display campaigns is calculated on a site per site basis.  Meaning the same ad variation could have a great QS on one site, and a bad one on another.