OS upgrades, sure, just use two systems with one of the existing async rep solutions between them. You'll need to make the master read-only for a brief period before failover as the slave "catches up" with the master.
Online PG upgrades aren't (until now) possible because the binary log format changes. But pglogical (which underpins BDR) solves this issue: https://2ndquadrant.com/en/resources/pglogical/ Process would be the same as an OS upgrade (brief period of read-only availability required), but you can do it on one machine.
Online PG upgrades aren't (until now) possible because the binary log format changes. But pglogical (which underpins BDR) solves this issue: https://2ndquadrant.com/en/resources/pglogical/ Process would be the same as an OS upgrade (brief period of read-only availability required), but you can do it on one machine.