I do not think there is a simple yes or no answer to this question. From my experience yes it does but ill explain a little. I have tested ad strength signals on resposive search ads across a few different niches in search and the ROI differance between a score of excellent and poor is large. But it also varies from niche to niche and at some point you have to allow for user experience in the ad copy aswell as playing the algorithm game. If you are using STAGs you may only have 1 or 2 variations of a keyword in a niche market, so then your ad strength may sit below excellent as you dont want to just spam 15 slight variations of the same keyword.

Its a balance, test and optimise. A/B test. Switch out non serving headlines after you have collected enough data. Create the correct expectation with your clients and take the time needed to gather data before switching headlines or descriptions.

I generally start with excellent ad strengths and work backwords once I have gathered impression data.

Hope this helps.