On the server side, I don't think you can distinguish between the Outlook Desktop (i.e. not offline access) client and the web client, as the server requests are the same. If they use the Outlook Laptop (with offline access) you've got more chance because the .aspx pages are served locally on the Outlook client.
However, I don't think you'll capture any metric that's more useful than just asking the users - I don't think this is a question for which there's a technical solution