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You should be sorted so long as you have a single database server that stores important bits of data for the Android app (i.e. username / password, user profile etc).
Once you decide to implement the web front end, you simply need to setup your favorite web-stack framework (Spring, Struts etc) to interact with the database server.
If you want to make updates using the web front end and push them to the mobile app - you will need to implement push messaging. Google Cloud Messaging (https://developer.android.com/google/gcm/index.html) works great and is salable.
If you don't want to use Google cloud messaging you can try to implement your own Sockets - but this can be quite difficult to manage.
Warning : I am pointing you to an app that I have developed
Have a look at this app : https://play.google.com/store/apps/details?id=com.loctracker.android&hl=en
The implementation is essentially what you have mentioned above : "Implement the whole system as a web application and wrap it into an Android app, effectively using the Android app just for the location information and little more."