Perhaps you would like a hint of bleach spots as a style?
I don't know if you can bleach colored to white. According to this: www.influenster.com/
I don't think it will bleach evenly. You could try making a design with your bleach pen
I think most answers on Google will be on how to whiten already white (but dirty/dingy) sneakers. Bleach does tend to weaken fibers but then people use it all the time so I guess it is left up an individual to decide to use it or not.
Some other links to check out.
I tried bleaching a similar pair of KEDS once when I was younger and it just turned to a weird peach. I don't think it would go to white based on my experience.
Since your shoes are still new I would not risk bleaching in case it does not turn out as you like.
Perhaps bleach them when your shoes are worn and you would not mind if they did not turn out as thought out.