From the android documentation : http://developer.android.com/reference/android/app/DownloadManager.html
The download manager is a system service that handles long-running HTTP downloads. Clients may request that a URI be downloaded to a particular destination file. The download manager will conduct the download in the background, taking care of HTTP interactions and retrying downloads afterfailures or across connectivity changes and system reboots.
As it is a system service, it depends on the android internals to make a call when to stop it and as your download is already enqueued, it shall try downloading again once restarted, till the staus is either STATUS_SUCCESSFUL or STATUS_FAILED.