Every now and then we get a book for review at www.popularscience.co.uk that attempts to do just this. A good example was the novel Pythagoras' Revenge by Arturo Sangalli. The idea was excellent and Sangalli nearly achieved the desired result. It genuinely did put across the maths (in this case) in a more approachable way. Unfortunately the fiction itself wasn't great. And this seems to be the challenge that most attempts at doing this fall down on. Either the fiction is poor, the science isn't very good, or the whole thing comes across as too worthy and dull. It is clearly very difficult to do well.
So I had mixed feelings when I got a copy of Litmus, a collection of short stories illustrating science themes. You can see what I thought of the book by following the link to the review, but in summary it was another worthy failure. Many of the stories were either not very good, or so full of their own artistry that they obscured the science. The book tried to get around this by following each story with a little explanation of the science and historical context, but this made things worse. It broke the flow of the stories and poured on a rather condescending dullness.
I don't like to admit defeat in anything that is being used to popularize science. But I am beginning to think that using fiction to get across the message is doomed to failure because you have two such contradictory aims. Something rather similar seems to happen on TV show QI when someone on the panel who is into science starts to expound a little on a science subject. The other panellists typically start acting bored and the whole thing falls flat.
Don't get me wrong, there are lots of ways to get people more aware and informed about science that can entertain and inspire. But I'm not sure writing fiction with a science context is one of them. Science in fiction is fine - but as soon as it becomes 'education about science in fiction' it falls flat.