Google "SPLIT BRAIN SYNDROME IN RAC"
You can check this support note as well
What is Split Brain in Oracle Clusterware and Real Application Cluster (Doc ID 1425586.1).
You should be shutting down your databases during maintenance because like I said nobody will be able to access it anyhow.
As mentioned earlier, if public network is down then why have the cluster up during this activity.
If your RAC nodes use ntp time server (as opposed to ctssd) then you'll have evictions as nodes won't be able to access the time server over the network.
If you use NAS for storage then you have to bring down the cluster for this activity.
If by network you mean public network, then the RAC should be unaffected. The database instances (as with the rest of the server) will loose outside communication. Cluster services instead rely on the Interconnect and shared storage, and that should still be available.
Exceptions to this would be if the cluster is using the public network for some cluster service - e.g. ocfs2 is used and the ocfs2 heartbeat is run via public IPs. Node fencing and eviction will occur. RAC/CRS will be directly affected if ocfs2 is used as OCR and voting disk storage.
Also, RAC does not need outside communication to do work. There are the DBMS_JOB and DBMS_SCHEDULER interfaces, and these can still happily execute workloads without communication to the public network.