I take back what I said earlier, it looks like they do not share state information. I think I misunderstood what I was reading yesterday on the forums.

I found the 890 Pro manual with a google search for "secondary harmony 890 Pro" at [Link: smarthome.com]
Now, after reading the section "Using Multiple Remotes and RF Wireless Extenders" on page 10, it seems that the primary remote only communicates with the second one to use this Z-wave network for the extenders and lighting devices.

I think I got confused with what's on the next page, how the 890 pro lets you set different rooms locations to keep from having the remote get the state information wrong. I forgot these two features unique to the 890 pro are separate and that state info has nothing to do with the Z-wave network. While it might be technically possible, it might be prohibitively difficult for them to have put in such a feature.

Apologies for getting your hopes up about it.