A species is defined by the ability to reproduce viable offspring, so any two plants within a species generally have the potential to cross pollinate. Like any good successful mating, it requires the union of male and female contributions at the right time, same place. So absolutely, GE crops have the potential to cross with non-GE crops of the same species—if they manage to get it on through time and space.
So the rules that apply to dogs and teenagers also apply to plants—keep them apart and don’t put them in the same place when reproduction is most likely. The major gene flow problems of the past stopped when they cancelled Plant Prom.
The whole discussion of GE gene flow really applies only to corn, soy and canola. They are the major food crops where outcrossing might affect others with a cross-pollination event. Sugar beets aren’t grown to flowering typically, so not an issue there. Virus resistant Hawaiian papaya has cross pollinated with others, and even many feral papayas contain the virus resistance gene (Manshardt et al., 2012 Acta Hort 124).
Why does it matter? It only matters if adjacent farms are growing a crop for a non-GE market, so presence of a GE trait in that product could jeopardize its sale. There is no evidence that gene flow from natural events invokes litigation.
As mentioned earlier, other factors and practices can prevent gene flow from happening. In corn, pollen is heavy and usually drops from the tassel to the silks, so even in a stiff wind it does not travel far. With corn, a simple buffer zone is sufficient to limit cross pollination. Knowing your neighbor helps, and friendly communication about planting/flowering date can limit cross pollination, as plants that are not flowering in synchrony are unlikely to cross-pollinate.
And finally, the added traits in the GE plants could be passed on to the next generation. If the seeds were planted the plants could possibly (but not certainly) exhibit herbicide or insect resistance. The herbicide resistance would not matter unless the herbicide was applied. Insect resistance could help that plant survive better or provide a higher-quality output, but non-GE fields usually undergo regimens of chemical insect control, so the trait would be meaningless.
In general these traits are just a few of 40,000 in the plant, so a much bigger threat to adjacent plant’s genetic integrity doesn’t come from the GE trait, it comes from the 40,000 other genes. That’s why farmers buy dependable and tested seed with known genetic content at the beginning of every growing season.