You likely should talk to your IT department. I know some places I've worked, if you didn't have permission to "light up" a personal device on the corporate network and you did so, it was grounds for dismissal.
The watch only supports 802.11 b/g/n at 2.4GHz. If your work is using exclusively 5GHz radios, you're sunk. If they're using 802.11AC, you're sunk. If they're using mac address filtering ("white listing to allow access") and only corporate devices are allowed, you're sunk (unless work actually bought the watch) 🙂
There could also be some enterprise security standards that aren't supported on Watch, but I haven't heard of them yet.
Start with your IT department - usually you can find someone helpful at their helpdesk. 🙂