The setting in your screenshot is for which contact picker AquaMail will launch when you press the "pick contact" icon(s) to the left of each address entry field.
By default it will launch its own contact picking window (which doesn't care if your phones' contacts come from Gmail or anywhere else) -- or you can launch the system contact picker from the menu.
Switch the setting in your screenshot -- and this logic will switch too.
One more thing -- the address entry fields have autocomplete, based on lookup in system contacts... again, the code doesn't care if your phone's contacts come from a Gmail account or somewhere else, the autocomplete should still work (after two characters).
If something doesn't work, please be more specific about what it is, thanks!
