This depends on the device you're using and whether your device is connected to the internet.
AirPlay
You will be able to AirPlay downloaded workouts to your TV if your iPhone or iPad is connected to the internet via WiFi. If your device doesn't have a WiFi connection, you won't be able to AirPlay downloaded workouts to your TV.
Chromecast
It isn't possible to cast downloaded workouts to your TV via Chromecast at all. Because of how Chromecast works, you need an internet connection to cast workouts to your TV.
It isn't possible to cast downloaded workouts to your TV via Chromecast at all. Because of how Chromecast works, you need an internet connection to cast workouts to your TV.