Is it possible to use a single device CAL to the Azure Appliance?
No.
or would we need to license per user?
Yes
Nothing else will touch the SQL server directly.
Doesn't matter.
Your scenario is a "multiplexer", the middleware architecture, the count of user is important.
At all, this is a community forum for technical questions & issues.
For question regarding pricing / licensing please contact a Microsoft sales partner or licensing expert.
Call (1-800-426-9400), Monday through Friday, 6:00 AM to 6:00 PM PST to speak directly to Microsoft licensing specialist.
http://www.microsoft.com/en-us/server-cloud/products/sql-server/buy.aspx