The answer to that is NO. Each keyword has its own QS and this is calculated when the Ad is eligible to run.
There’s a misconception that there is an account, campaign and ad group have quality scores. That’s incorrect. Quality score (QS) is a keyword metric which shows how they’re performing for:
⁃ Landing Page Experience
⁃ Expected Click Through Rate
⁃ Ad Relevance
These three factors affect your quality scores. And it’s calculated each time your ad is eligible to appear in the auction. So, it’s calculated at auction time and not before or after.
When you first setup your Adwords campaign you’ll notice that your keywords have no quality score. That’s because they have not appeared in any auction result and therefore it cannot be calculated.
Paused keywords may have a historic quality score but that will have no significance because they’re no longer running. The quality score cannot be recalculated when they’re paused and will therefore not be updated. Neither will they affect your accounts performance as long as they remain paused.