You can spray it like that, but I really think you'll struggle to hand stain it in that subtle a sunburst. I've only seen a couple of stain bursts that approach a sprayed burst in terms of gentle colour blending. They generally end up with very definite edges.

If you really wanted to hand stain a burst you'd need to apply may many very weak coats and build up the density slowly. Because of this, I'd go for a spirit rather than a water based stain - though spirit stain and binding don't get on at all well.

It would be very hard not to stain the centre section at all, so I'd do a very weak all-over stain to start with. With spirit/alcohol based stains, it's easier to use an alcohol rub to merge the coats together than it is with water-based stains and a water rub. Start in the middle and work outwards, always using a new piece of cloth each time you start from the middle to avoid laying down stain that's been picked up by the cloth when wiping. However, there are limits as to how much post-application merging is possible and there are no guarantees as to how well it will work, so practising on scrap wood first is highly recommended. You may then decide that it's not practical.

Airbrushing the stain on should give better results, in theory, than rubbing, but I've never tried it, so can't speak from experience.

The example bursts shown will have been achieved by an initial all-over stain, and then spraying the darker colour(s) on using a clear lacquer. It's by far the best method for doing a burst. It's not that hard either, though you do have to remember to spray from the centre of the guitar outwards, aiming to just miss the edge of the guitar with the centre of the spray and letting the fan pattern of the spray provide the colour graduation.