have read that a summing amplifier circuit can be used to add a DC signal to my AC signal to achieve the DC offset (Figure 2). Is this correct?
It is correct but rubbish. All you need is two 10K resistors in seriese going from supply to ground. Then at the junction you wire it to the analogue input and a capacitor say 1uF.
The other end of the capacitor goes to your AC audio input. Also connect your audio ground to the Arduino ground.