Merkle-like hash tree that mirrors existing tree structure
Yes: this allows the root hash to authenticate the entire content of the directory tree so that, e.g., a malicious storage server cannot fool you into accepting a forgery replacing a file you previously asked it to store.  This is how Tahoe-LAFS is structured, or at least the immutable parts, and how ZFS block pointers are stored when authentication is enabled.  More broadly, there is a modest literature on authenticated data structures that are all built out of essentially this idea.