Yes companies can monitor all the traffic on their network. They don't typically read everything that goes though but look for certain hot button words like hacking at least this is what they do at universities. You get assigned an IP when you log on and everything can be tracked to that IP....now they have no way of knowing what IP your phone has unlike your desktop which is company property and most likely has a static IP. But if you put identifying info like if heather is your real name then they can associate that IP and all you do with heather.