Yes, I believe you can. A couple of options are as follows:
Draw your 'map figure' in an overlay - if the background is translucent, then you'll be able to see the Google map underneath.
Alternatively, use a dummy Google maps API key - in this case the MapView layer is rendered as a grey background but all the API calls appear to work. Again render your 'map figure' in the Overlay draw method.
In both cases, you'll have to ensure the map projection (scale, position, etc) match up with the coordinates of your 'map figure', especially if you scroll or zoom the map view.
It might be best going with the first option, initially, then you'll have a visual confirmation if you're code is correct.