Can I use Apple TV app on multiple Roku devices in my house

Quick search for terms and conditions:

For any Service, you can have up to 10 devices (but only a maximum of 5 computers) signed in with your Apple ID at one time, though simultaneous streams or downloads of Content may be limited to a lower number of devices as set out below under Apple Music and Apple TV content. Each computer must also be authorized using the same Apple ID (to learn more about authorization of computers, visit Authorize or deauthorize your computer for iTunes Store purchases - Apple Support). Devices can be associated with a different Apple ID once every 90 days.

Legal - Apple Media Services - Apple

Further down:

Apple TV Content:

- For most channels, you can stream video Content on up to three devices simultaneously. 

- Learn more about Apple TV Content Usage Rules at Download and stream shows and movies from Apple TV+ and Apple TV channels - Apple Support.

You can use the Apple TV app on as many Rokus (and other devices that support the Apple TV app) as you want, but there are limits to the amount of simultaneous streams per subscriber: 6 simultaneous streams for Apple TV+.

Don’t own a Roku device.

Try it and see.

Post back and let us know.