Does an HA Loki instance need persistent local storage?

I have been running a cluster of Loki instances for about two hours. They are not under live load, but they seem to be running well. I have storage set to use GCS. The GCS is the only form of persistent storage at the moment. I have removed the persistent volume. Anything that the Loki instances write to local disk will be ephemeral. I have deployed new instances and killed old instances several times and I am not seeing any fatal errors.