Ok, I'll answer in two parts

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Design-wise (I talked this over with Trent and he agrees here), the way you are doing it sounds best. For your student users, a web interface is the way to go. There would be too many deployment issues and everything else trying to get a smart client app pushed out to thousands of students on all types of machines. For the administrative interface, a smart-client app would be best. You'll be able to develop the more complex administrative functions more quickly, and it will offer more robust tools on the end-user's side as well.
Licensing-wise, you'll need 1 ES CAL for each disperate administrative user that is going to be connecting to your database through ES. So if you have 120 administrators that are talking to your server, that's how many ES CALs you'll need. Since the student web portion will be housed completely on your server and therefore won't be communicating to the SQL server through ES, you don't need to worry about them from an ES licensing perspective. From a SQL server perspective, while it is true the ES will "bundle" the connections so that SQL thinks it is only a single user, you still need 1 SQL CAL for each of those disperate administrative users to stay kosher with Microsoft. You do NOT need to buy a windows server user CAL for each of the administrative users, however. You are communicating through the web (ES), and as such, you don't need the local user CALs.
The synchronization issue doesn't really come into the ES licensing, since the nuts and bolts will be done on the server itself, but I do feel your pain from a design standpoint. That kind of synchronization is never easy to pull off cleanly, so I'd do everything I could to try and sell those schools out of wanting to house their data local. I know that in the real world you can't always keep your customers from insisting on something silly, but we've been down that road many times in our medical application, and avoiding it in the future is one of the main reasons we developed the enterprise server. So here's hoping
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