As far as I know it does not. I have Prime and it doesn't seem to be linked to my usage. There is mention of using Mobile devices and that does get charged against you usage:
Data consumption when using Prime Video app
When using Prime Video app on Optik TV or your mobile devices, it will contribute to your data usage. High Definition (HD) content uses about 3GB per hour.
Source:
Amazon Prime in your Optik TV package | TELUS Support
Just a long time customer hoping to help.
