If you’re turning left on a Green Light, then YES you should pull into the intersection when you’re waiting (under normal conditions; which are, there is an open space for your vehicle to fit into once you turn).
This lines up your vehicle so that you have a short turn across traffic. There are also legal implications. When the light changes to yellow or red, you’re allowed to exit the intersection, and you should turn only when it is safe, regardless of the colour of the traffic light. (It could be green, yellow, red, pink, purple or brown by the time it’s safe. The point is, do not turn until it is clearly 120% safe to do so.)
If you do not enter it
If you don’t pull into the intersection when the light is green (i.e. you’re waiting behind the white stopping line) then legally you aren’t allowed to leave the intersection once the light goes yellow or red, and you either will potentially be there all day long or you will be breaking the law and potentially being dangerous by turning once it’s yellow (because it is such a longer turn – you will probably surprise others by turning).
2- Way Stops
The same applies for a 2-way Stop (sign) intersection when you are on the through street and are turning left and waiting for oncoming traffic. If you don’t pull forward in this case, drivers at the stop sign may think you’re just a really nice person and you want them to go first; and that would be totally backwards. Isn’t this the whole point of stop signs? People facing stop signs are supposed to wait for people who are not facing stop signs. If you pull forward a bit, you’ll be in their way, and they will understand – even if they have no idea how to drive – that you will be going first. Pull forward so you have a short turn across traffic and to avoid confusion. Collisions can happen when people are confused.
Keep the car straight (generally)
Remember to keep your vehicle and your wheels straight when waiting in case you are ever rear-ended. If you get pushed straight forward, it’s probably not the end of the world. Compare that with what would happen if you were pushed into oncoming traffic and consider the consequences.