I confirmed this when I tested my Plex server on a Raspberry Pi out in a cabin in the middle of nowhere and it streamed fine without an Internet connection.
Only hiccup was the Roku client took unusually long to bring up my list of local content; I could imagine it timing out on DNS connections.
I've never connected it to the Plex servers ("associated it with my Plex account"), perhaps thats the difference?
Maybe that behaviour's fixed now, or maybe I just hadn't found the setting mentioned in the comments below.
To answer your question, yes it appeared to be attempting to authenticate with their servers, even though my Plex server was local
Local Auth only.
AirPlay seems like a good local alternative, but I’m hesitant to fully invest in it because it would lock me into Apple products and I fully hate to be locked in, despite having an iPhone at the moment.