Yes. Dropbox Carousel support videos as well as photos. Videos in your Dropbox appear in your Carousel right alongside your photos. In your Dropbox Carousel, you will see a video with a "Play" icon. Just like your photos, you can view and share your videos.
Following are the video file extentions that are supported by Dropbox Carousel: .mov, .mp4, .m4v, .mkv, .avi, .wmv, .flv, .asf.