I have an app that needs to do an intensive database operation on start up. The app holds a local copy of the contacts on the phone and synchronizes with the android contact
Use getStatus() to get the status of your AsyncTask. If status is AsyncTask.Status.RUNNING then your task is running.
AsyncTask
EDIT: you should reconsider your implementation and hold the AsyncTask probably in a Service or IntentService to fetch your data from the web.
Service
IntentService