Windows Phone (as well as iOS) do in fact turn off wifi when the screen is locked. Two caveats for WP are:
First, if it's plugged in, it keeps wifi on (don't know if it's also true when wirelessly charging, but I suspect so). Second, of any app is relying on a continuous data stream that has been initiated on wifi (such as music streaming), it will keep the wifi on for the duration of that stream.
My suggestion to you would be to have it charging while you're at work (if you're at a desk). If that's not an option...you're out of luck. You'll have to either manually turn on the screen every once in a while or just keep 3G/4G on:(