ANSWER: Yes, but only for Enterprise level clients, along with its dependencies (Git, etc).
More info here: https://www.littlebizzy.com/faq/git-support
However keep in mind that using VersionPress as a remote staging service is not really possible yet, because their current release require WP-CLI (managing via SSH) and do not offer a user interface yet. We are following this closely, and may end up offering something related in the future.
More info: https://blog.versionpress.net/2016/11/remote-workflows/