Will a diode conduct if one side is floating and one side has voltage applied to it?
With the charger disabled by SW1 the diode will conduct and produce a voltage on the cathode of about 0.5Volts lower than the 7V battery. Under heavier load conditions this volt-drop might be a little higher. Under lighter load conditions this may be a little smaller.

BTW diodes don't have a "V_cutoff" they have a forward volt drop.