No, you can only watch your downloaded workouts on the device you downloaded them to.

That's because, when you download something, you're taking it from the internet and storing it on your device. That way, you don't need an internet connection to watch it because it's stored on your device. But because it's stored on that specific device, you won't be able to access it on different devices. 

You can download the same workout onto multiple devices if you need to.