If your campaign is opted into show ads on the Google Display Network, and your Display Network ads have a lower CTR than your existing search ads - Will this impact the quality score of your search campaign or not?
Re: Quality Score
I think there are multiple posts on this question - https://www.en.adwords-community.com/t5/Tracking-Reporting/Quality-score-of-search-and-display-resul...
Per Dave & Moshe's answers, no, your Display Network CTRs will not impact your Search Network Quality Scores. The two are completely separate. I'd recommend that you segment Campaigns by Network - one Campaign for Search Network, and one Campaign for Display Network.