So, the main question here is how likely life is to evolve in a situation like this (assuming a stable orbital system). The answer? Not going to happen.
The green band is definitely do-able, though you'd get some really, really weird seasons. "Summer" would be defined as the time when the sun(s) never set, "Winter" would be when the two suns are lined up and you actually get a half-day of darkness. You would, of course, need to be a minimum safe distance from the secondary star in order to not have your water boil off, but finding the Goldilocks spot would be possible.
The problem, as it turns out, is not with the arrangement of the system. The problem is the Hypergiant you are hanging out in close proximity to. Hypergiants have...problems.
The first problem they have is that their ridiculously high energy levels are such that it can exceed the Eddington Limit. The Eddington Limit is the point at which the star's luminosity is so great that the radiation pressure pushing the star outward meets the gravitational force holding the star together. A Hypergiant like VY Canis Major is literally so bright that it is blowing itself apart. It is estimated that at this point, Canis Major has shed nearly half of its original mass in this way, hurling it away as a sort of super solar wind. If our planet was far enough away, it may be able to survive this particle onslaught and, as you said, the habitable zone for VY Canis Major is very, very large.
The second (and most critical) problem is that they don't last very long. The lifespan for hypergiant stars is measured in millions of years, as opposed to the tens of billions for sun-like stars, and much longer for red dwarfs. So, lets assume an absolutely ideal situation...suppose our Hypergiant, its orbiting star, and the planet candidate all formed within a few years of each other (the bigger star would have formed first, and gobbled up most of the material, only leaving a smaller amount for the secondary star.) So, let's suppose everything happened just right.
It is estimated that our sun is about 4.6 billion years old, and Earth is supposed to be about 4.54 billion years old. As we are the only standard we have for the formation of life, we have to use our own development timeline. On Earth, the most basic prokaryote-like life supposedly formed 2.9 to 3.5 billion years ago. This means that the sun had already existed for between 1.1 and 1.7 billion years by the time the most basic of life was forming. This is far in excess of the life expectancy of a hypergiant. Furthermore, it took us about 4.54 billion years to reach the point of 'advanced intelligent life,' which is immensely beyond the lifespan of such a star.
In fact, the time between the formation of the Earth and the theorized 'great impact' that created the moon is too long (~500 million years).
So, there's why it couldn't happen...the star would have lived its brief, extremely violent life all the way from birth to whatever horrific death awaited it (probably a hypernova that would obliterate its child star before it collapsed into a black hole) long before life could have evolved around it.
Supergiants are a little better, but still tend to go boom after only about 30 million years. Still not anywhere close to long enough.