Yes, it should be possible. TwitterKit allows to create custom requests to the Twitter REST API.
Tweet media can be uploaded in a 2-step process:
- First you send each media to Twitter by calling the
POST media/upload method and collecting the returned media ID.
- Post your Tweet by concatenating all media IDs to a comma-separated list and using this list as
media_ids parameter when calling the POST statuses/update method.
More documentation for uploading media is available on the Twitter Developer site.