No it wouldn't. Cancer expresses fundamental genes critical to all multicellular organisms. That is already known so the fact that cancer expresses 'older' genes doesn't prove anything.
It is very clear from the press release and also form his own article on his 'theory' from 2011 http://www.guardian.co.uk/commentisfree/2011/apr/25/cancer-e... that he doesn't understand evolution.
Consider this nugget of wisdom that is 100% pseudoscience: A century ago the German biologist Ernst Haekel pointed out that the stages of embryo development recapitulate the evolutionary history of the animal. Human embryos, for instance, develop, then lose, gills, webbed feet and rudimentary tails, reflecting their ancient aquatic life styles.
That is wrong, it has been know to be wrong for a hundred years at least and basing a theory on it is ridiculous.