Yes you can easily transform standard WordPress galleries to immersive full-screen experience without installing Jetpack and connecting to WordPress.Com
Gallery Carousel Without JetPack is a free WordPress plugin that is made by forking the carousel module of JetPack and this forking makes it useful for the users who are not using Jetpack in their websites. This plugin transform standard galleries to an immersive full-screen experience having comments and EXIF metadata.
Simply install and activate this plugin then visit your WordPress Admin Area Dashboard -> Settings -> Media for more options.