Indeed Icenium can help you utilize the camera of a mobile device and there is a BarcodeScanner plugin that could be used for scanning a barcode. Sending data from mobile device to your server is easily accomplished by exposing your data via a web service and using jquery ajax requests. In short creating a hybrid app that scans a barcode and sends the data to a server can be accomplished.
However in order to know which is the user that scanned specific barcode, you would have to implement some kind of authentication. The user would also need to have your app installed (or the link should point to the app in the respective App Store so it could be installed).
Technically speaking there doesn't seem to be a culprit to prevent you from achieving the scenario you described, however the workflow is a little bit unusual. Users tend to be given the option to either browse your site or do their thing through an app on the device. Switching between both could be confusing and undesired.
You've missed the Icenium Visual Studio Integration keynote? It has been recorded and posted here.
Looking for tips & tricks directly from the Icenium team? Check out our blog!
Share feedback and vote for features on our Feedback Portal.