Yes you can do that by just creating a BroadcastReceiver
that calls your Service
when your Application boots. Here is a complete answer given by me.
Android - Start service on boot
If you don't want any icon/launcher for you Application you can do that also, just don't create any Activity with
<intent-filter>
<action android:name="android.intent.action.MAIN" />
<category android:name="android.intent.category.LAUNCHER" />
</intent-filter>
Just declare your Service
as declared normally.