Hello @davidjedd,
Although we cannot say with certainty that this will work, we can provide some instructions on how to configure the Apple TV 4 to learn new device codes. It is important to note that the SoundTouch 300 accepts IR commands from remotes.
The easiest way to see if the system would be compatible with the Apple TV remote would be to go to Settings > Remotes and Devices > Volume Control, then select "Learn New Device" and follow the prompts on the screen.
Let us know if that helps at all.
Thank you.