This video should answer your questions. You may also want to read this thread:
www.seabreeze.com.au/forums/Kitesurfing/General/Self-rescue-experiment-methods-comparison/We have many hundreds of successful practical self-rescues being done by our students in deep water every season using this method, and all in cross-shore winds. Although most of them are done without the board.
As you can see in the video you can use your board as a rudder to help increase your speed and direction during the rescue. In the video I cover 200 meters of distance from the shore, in cross-shore winds, in about 5 minutes. I have also witnessed one of my ex-students self-rescuing from 1km out in a cross-shore 18 knots breeze, came back with his board within 30 minutes and only lost about 300 meter of ground downwind. This can only be done with a perfect sail / board rudder combo.
The key is creating an efficient sail, which many people struggle to do, from lack of knowledge and practice. If you choose to wrap your lines (good luck with this in strong winds) it can be easier to keep your board in your feet in front of you, otherwise if you choose not to wrap your lines, take the board off your feet and simply push the board forward as you pull yourself to the kite (as per video above).
Whenever you get a new kite, pump it up without connecting the lines and practice creating the best sail you can with it on the beach, then take it in the water (still without the lines connected) and create a sail with to practice. Every kite is a bit different when comes the time to creating a sail with it. Some kites are equipped with Self-Rescue handles which are very comfortable but less powerful than using the bridle or upper center line. The key is not to use the wing tip line (steering line), which I see many inexperienced people do. This will also create a sail but will blow you mostly DOWNWIND!
When choosing to self-rescue without wrapping the lines, the most important thing is to resist the
natural reflex to kick your feet and swim at any times during the entire rescue. This is the main difference between no tangles (or very few tangles) and a s**t load of tangles. 95% of our students practicing self-rescue for the first time have their lines untangled and ready to go again in less than 10 minutes, when paying attention to the no swimming, no kicking rule.
Unfortunately, few kiters are actually competent at self-rescue simply from a lack of practice during their lessons are no practice after their lessons.