Incognito mode does nothing to obscure your network traffic, so its contents and recipient are always apparent.
Supposing that you use a HTTPS encrypted connection, the contents would theoretically be obscured... but not the recipient. In this case they might be able to guess that you are chatting by what domains that you request information from, say a bunch of requests to hangouts.google.com. Then again, someone would probably need to be looking. You might be able to claim it is a side effect of simply logging into gmail.
If your employer is more draconian they might MITM all HTTPS traffic with a "in house" root certificate on their computers. In this case they could see everything you say, and have a product that likely captures such statistics.
They may even install monitoring software on the computers that spies on what you do directly, possibly even viewing the screen or capturing keystrokes.
In summary, if it really matters, they can possibly tell, and you really should not use hangouts.
They have no idea what you do on your phone over a cellular data plan...