Yes you can.

Please install the Big Team Challenge iPhone app first, then install the Apple Watch app. The Apple Watch app shows your step count for today along with your team’s total step counts.

Please note: The watch app will not automatically sync your steps to the challenge. If you wish to sync your steps, follow the instructions here.

If the Apple Watch app isn't showing your challenge information, open the Big Team Challenge iPhone app, go to Settings, then tap Apple Wacth app. This will ask for permission to Big Team Challenge to read your Apple Health step data.