No, private projects are, by definition, private. These projects are created under the folder My private projects. They can only be viewed by the owner unless the user joins a group that prevents members from having private projects, which will allow the administrator(s) of the group to view these projects after they have been incorporated in Group projects.
The shareable projects are projects created under the folder Group projects. They are visible by default to the group administrator(s) and shared among team members by changing share settings.
However, if you want to share the content of a private project to members of a group, you can:
In the advanced labfolder version, the group settings for your group can be set in a way that no private projects are allowed. If you do so, all private projects of newly invited group members are moved into the respective group.