Sure, but if it’s anything like MeshCore, a few observer nodes will be able to see which repeaters the message first entered the network from and from that know roughly where it was located.
The worst part privacy wise could be the announce packets which include a hop count and the address for the origin so if you had enough interfaces you could roughly say where a node is on a network graph (geo locating that is an entire other problem)
Privacy also depends on what interfaces you communicate over, eg TCP reveals IP addresses to the nodes you directly connect to (combine with hop counts to see if a packet definitely originated from that node), LoRa gives an idea of how close it might be because of its range limits and the fact radio emissions can be located.