The short answer is, No. Doing so is a violation of the Google Maps Terms of Service:
https://developers.google.com/maps/terms
Check out this FAQ as well (especially the part about acessing the maps and satellite images directly):
https://developers.google.com/maps/faq#tos_tiles
Apparently the only way to do this legally is to use the Google Static Maps API.
While not immediately relevant to Android, Rex Hansen posted a nice blog about doing this using the Silverlight API:
http://rexdotnet.blogspot.com/2010/09/use-google-maps-with-arcgis-silverlight.html
Hope this helps.
Thanks a lot!
But I still have one doubt. Can't I use both google maps API and ArcGIS Runtime for Android in one project? In that way, still can't I do it?