Hi Ashvin,
The title of your question and the question itself are two separate questions.Regarding the title - yes AC does require a return path and as Giovanni mentioned, the return path in your house is the neutral. And as he also mentioned the earth wire is there to protect you should the live/phase/hot wire come into contact with exposed metal parts etc.In remote areas of certain countries, high voltage transmission is provided out to those remote areas via a system called SWER. Single wire earth return. It saves running a neutral conductor and therefore money but can have issues due to ground resistances.
Regarding the question. An energised conductor with a voltage, an AC voltage, will have electrons changing direction at whatever your countries frequency is, even if it has no return path. You need a second conductor, a neutral or earth conductor, to complete the circuit to allow current to flow. Current will not "flow" without a circuit but a conductor sitting in air not touching anything can have a voltage present. You will only get an electric shock if you hold an energised conductor, say in one hand and complete the circuit with the other hand by touching earthed mettalic parts or the neutral conductor for example. You could hold two energised conductors, one in each hand and not get a shock, as long as both conductors are supplied from the same source, same voltage etc( do not try this, take my word for it). And if you try to measure the voltage between them it will read zero, regardless of what voltage is present. If however you measure the voltage between one of the energised conductors and an earth conductor you will measure a voltage.Also the earth conductor and neutral conductor very often come from the same point, if you trace it back far enough, which is why you can hold the neutral and not get a shock, it is effectively the same as holding an earth conductor.