Architecture for a globally distributed Neo4j?

The distribution mechanism in Neo4j Enterprise edition is indeed master-slave style. Any write request to the master is committed locally and synchronously transferred to the number in slaves defined by push_factor (default: 1). A write request to a slave will synchronously apply it the master, to itself and to enough machines to fulfill push_factor. The synchrous slave-to-master communication might hit performance thats why it's recommended to do redirect writes to the master and distribute reads over slaves. The cluster communication works fine on high-latency networks.

In a multi-region setup I'd recommend to have a full (aka minimum 3 instances) cluster in the 'primary region'. Another 3-instance cluster is in a secondary region running in slave-only mode. In case that the primary region goes down completely (happens very rarly but it dows) the monitoring tool trigger a config change in the secondary region to enable its instances to become master. All other offices requiring fast read access have then x (x>=1, depending on read performance) slave-only instances. In each location you have a HA proxy (or other LB) that directs writes to the master (normally in primary region) and reads to the local region.

If you want to go beyond ~20 instances for a single cluster, consider doing a serious proof of concept first. Due to master slave architecture this approach does not scale indefinitly.