That’s indeed possible.
When you share a post on Facebook, LinkedIn or Google+, or when Jetpack Publicize publishes a post to your Facebook page / profile, Facebook crawls the page and looks for Open Graph meta tags in the head to build a complete post preview (with an image, title, description, …).
Jetpack automatically creates these Open Graph Meta tags for you unless you already use another Open Graph plugin, in which case we let the other plugin handle things.
If you do use Jetpack to manage Open Graph Meta tags, you can use the jetpack_open_graph_tags
filter to customize the tags added to each post or page:
https://developer.jetpack.com/hooks/jetpack_open_graph_tags/
You could consequently use that filter to unset the images added by Jetpack and replace it with an image you added via post meta for example.
You can use that same filter to change the output of the twitter:image
meta tag, used when sharing a post on Twitter.
I hope this helps.