The Play store doesn't exist on Windows Phones. Software downloads from the Microsoft Store will go over data if the download size isn't overly large. If its than it would have to be done over Wi-Fi.
If you go to the Store app and tap on ... and select settings you'll see a setting Only get updates over Wi-Fi, if the setting is on it won't download any software over you data connection, only Wi-Fi. If you turn it off it will use your data connection to get the update with the caveat that download size isn't large then it would have to go over Wi-Fi.
With all that said this wouldn't prevent your phone from connecting to your workpace Wi-Fi. If the phone doesn't see the network via settings > Wi-Fi then there's probably something with the network prohibiting Windows Phone.
