Yes, you can record and watch at the same time. 

While CloudAntenna recording, you can watch that channel live or Watch Anywhere.

To Watch Anywhere your recording while CloudAntenna is recording, please make sure you configure Watch Anywhere. Learn how to configure Watch Anywhere.

Once recording is complete, you can watch your Cloud TV recording anytime, anywhere, no special configuration is required.

Note: there is maybe a small delay between when your recording is finished and when its available for playback, as prepares to for playback on any device!