Can I use Cardiogram's continuous mode on my Apple Watch during a workout?

Yes, you can use both continuous mode and workout mode simultaneously. If you begin a workout from the Workout app, you don't need to click the "Start" button on the Cardiogram watch app. The Cardiogram app will automatically detect the measurements taken by the Workout app and display them in Cardiogram on both the Cardiogram watch app and the iPhone app.