It is possible. Make sure you select Option 4: Entire Site, Page/Post Featured Image or Option 5: Page and Post in Appearance => Customize => Header Image. This will make header image Featured image on the respective pages and posts.
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Any cookies that may not be particularly necessary for the website to function and is used specifically to collect user personal data via analytics, ads, other embedded contents are termed as non-necessary cookies. It is mandatory to procure user consent prior to running these cookies on your website.