Is it possible that organically grown crops can be infected by GM genes?
Yes. Organic standards do not allow the use of GM seeds and therefore steps are taken to try to prevent contamination. Tests are not required, although some vigilant organic companies require them. According to the organic standards, contamination by cross-pollination is not disallowed, but some companies reject contaminated product above some small amount such as 0.1%. Organic canola farmers in Canada sued biotech companies, since cross-pollination has made it impossible for them to grow organic, non-GM canola.