It's their network so traffic could be captured for them to check as it's their system.
As to files, usually not shared unless you sent them over the network.
Remember you are asking if they are able to. Not that it's not possible. It's possible but unlikely. Most business IT folk have other worries and don't have a reason to be a spy master.
I'm connecting to a wifi at work, is the network admin able to access my email if I have a yahoomail app on my fone and can he also see the files that are in my fone