for this type of planned maintenance, it may be better just to disable/unconfigure HA, and then enable again when the maintenance window is complete. However, for unplanned events such as an entire network failure. HA is smart enough to realize there is no heartbeat to any of the HA nodes, therefore doing nothing.
Also, just as a side Q, can I enable HA on a running cluster with lots of running VMs?
you just need to edit settings of the cluster and enable HA. From there the HA agents will be pushed to the ESX(i) hosts and your cluster will be configured for HA.
This process will not impact any of the guests
You hit a very important concern that is why best practice is to insure redundancy and isolation of the management ports to cover a network failure but the since scenario you describe will be a known event you will be able to go in and temporarily disable HA -
Yes you can enable HA wile a cluster is running -