Perhaps if your app handles the ACTION_ANSWER intent, you could display whatever screen you like. I don't think this will enable you to customize the existing screen, just replace it with your own.
For your app to handle intents you have to add intent filters to the app manifest file. This is fully described in the Intent class documentation. Here is a quick sample on how you could handle the ACTION_ANSWER intent:
<activity class=".MyCustomCallActivity"
android:label="@string/mycustomcall_title">
<intent-filter>
<action android:name="android.intent.action.ANSWER" />
</intent-filter>
...
</activity>