That might work as the diode from "7805 gnd" to gnd will increase the 7805 output voltage by the diode drop.
Also mind the 7805 needs at least 2.5V higher input to operate properly (see the datasheet). Moreover you are upping the required input voltage by 0.7volt (the diode in 7805's gnd), that means your power source shall be something like 8.2V min to make 7805 happy. You may consider so called "low drop voltage regulators" which require input voltage 0.2V higher than its output.
Btw, I doubt you can connect the 4x1.5V battery directly as depicted in your schematics - consider at least a charging resistor as a minimum (to limit the battery charging current).
Also mind the voltage at "arduino power input" will be 6V unless the battery discharges itself to 5V.
6V may damage your "arduino" system and related circuitry when not using a proper voltage regulator at "arduino power" input (ie when using your own bare metal design)!
And mind the Arduino requires some minimal power voltage (when talking UNO for example) so 5-6V at its input may not make the Uno happy.