Why not set a background to your ActionBar with the image in it (like a strip for the Action bar background with your image to its center, Nine patch would be preferred).
Then you can assign this as Action Bar background like,
<style name="AppTheme" parent="@style/Theme.AppCompat.Light.DarkActionBar">
<!-- All customizations that are NOT specific to a particular API-level can go here. -->
<item name="android:actionBarStyle">@style/MyActionBar</item>
</style>
and,
<!-- general styles for the action bar -->
<style name="MyActionBar" parent="@style/Widget.AppCompat.ActionBar">
<!-- Support library compatibility -->
<item name="android:background">@drawable/actionbar</item>// your nine patch image
<item name="android:icon">@android:color/transparent</item>
</style>
You can then hide the Title as well. This is not a hack but considering you don't wanna temper ActionBar this will work. Have fun :)