Hi Chris.rogers,
If I understand your query correctly, that you are willing to see the documents on cloud that you have scanned using Adobe Scan app?
You must save your scanned document to the "Document Cloud" to, only then you would be able to access that pdf file from web or your desktop application.
Here are the steps for how you can save the scanned file to Document Cloud- Scanning Documents — Adobe Scan Help || Scanning Documents — Adobe Scan Help
You may check your files on "Document Cloud" storage on web- Adobe Document Cloud , Sign In with the same Adobe ID and password.
Regards,
Akanchha