In a 12v automotive system, can a second battery properly sustain charge with a diode?
Yes, that configuration is viable.  As the commenters suggest, a better (lower Vf) diode is advisable.
This is similar to how car audio fanatics configure their systems.  They have a seperate battery (and capacitor) bank that is powered through a large diode, and a diode to the main 12V battery so that neither system will adversely affect the other.  eg. when starting the engine, or when they are cranking the volume their headlights won't dim.