Is it possible to configure OneTeam app on the iPhone to connect with a private, corporate OpenFire server?

yes, you can certainly do that.
Make sure if you have trouble you visit the advanced setting page.

I have OneTeam connecting to my private openfire server. 

Had to specify numeric ip address as there were dns issues.

Also, I have to disconnect from cell network to make it work.
Airplane mode on
Then re-enable wifi
Then log in to VPN
Then launch OneTeam and use it
Then remember to quit airplane mode and VPN

If there any way to prevent having to go to airplane mode?