Direct answer
Can Unwanted Subscription read iCloud Mail?
No. There is no iCloud inbox connect. Apple does not allow it for apps like this. Your iPhone Settings list still shows Apple-billed plans. For Netflix, Spotify, gyms, and the rest, upload a statement or connect Gmail or Outlook.
What you can do
Three paths that still work
Privacy
We will not ask for your Apple password
Any site that asks you to type an iCloud Mail password into a subscription app is the wrong kind of product. Unwanted Subscription does not offer that field. Details are in the Privacy Policy and FAQ.