Good question. It is possible to do that, but you will need to replace the featured image functionality with something more custom. Here’s a snippet that I used creating a child theme for a hospital that was using the Foundation theme.
(See support site for snippet)
In the child theme, we created a folder called images and placed the seven banner images there. Then this snippet was added to the header.php file in the child theme. It uses javascript to randomly load one of the images into the new div with the id of “banner-image.” I used javascript instead of php so that the customer could still use caching while not losing the random images.
In Bottega, you could copy the layouts/post-formats.php file over to your child theme. That’s the file where the featured image is set in Bottega. If you’re not ever going to use the video, slideshow or featured images there, then you could replace all the code there with the snippet above. If you’d like to preserve that ability, then you could set the random images as a fallback. That would look something like this:
That’s one possibility at least. I haven’t tested this in Bottega, but that’s where I’d start.
Have a great weekend,
Bill