In the picture above, this is asking if the left side of the hand touches the right side of the neck, and if the violin's weight rests against that side of the hand at all (I'm clearly a big fan of Sean Lee, as I've stolen a frame from another of his great videos).
First, a dose of common sense: Your chin is there for a reason. Use it to hold the violin in place! Don't exclusively rely on the side of your hand to hold up the instrument like beginners do. If your neck is weak, tough luck. Maybe you should play another instrument, practice more, or hit the gym for once in your life.
This being said, I've asked a lot of great violinists and violists, and the answer to the question above is absolutely yes. It stabilizes the hand so much that once you get used to it, it'll be hard to imagine how you ever played in tune without this technique (if you ever did). Except for high positions (noobs: when your left hand is close to your face), this generally applies to shifting too. Even on double stops, try to stay in contact with the neck when you can.
Again, use common sense. In high positions, with wide vibrato, or in moments of unusual awkwardness, back the hand off a little. Be sensitive.