GPS time for network on private channel

I understand that the GPS can supply time for the entire network. What I dont know is if the GPS reports position on a private channel, does it still provide that time to the rest of the network if they are not configured with that channel?

no,
if the gps node is only in one private channel, it only reports data to this channel.
more correctly : the gps data and most other data -including time- are sent out channel-specific encrypted , so that only same channel nodes can decrypt and read.
other channels (including default channels) cannot read.
just a very small part of a broadcast is unencrypted header.

there are some more options in newest firmwares about channels and position data, i have not checked yet…

Thank you Kilroy, Very informative!