Howdy Kurtis,
That would certainly be possible with a theme override. The Themer’s Guide walks you through how to make overrides like that.
If I were you I would override events-calendar-pro/src/views/pro/week.php and add your image in there. You could add a simple
tag and link to a static image. Or if you wanted to be able to adjust the image from the backend, you could create a new page called something like “Week view’s featured image”. Add a featured image to it and hit save. Grab the page ID # from the URL. Then user tribe_event_featured_image( $page_id ) to show the featured image for that page. Thus any time you want to change the image, just go to Week view’s featured image and update teh featured image from the WP backend.
Does that all make sense? Will that work for you? Please let us know.
Cheers!
– Brook