Oil refineries use natural gas, just as all big consumers of stationary heat do. You always take a lower value, less dense fuel to make heat, and use the higher valued fuels, ethanol, gasoline, diesel, bio diesel, as transportation fuel with their very high weight/volume to energy ratios.
It would be foolish to use these fuels to just make more of the same fuels.
The new versions of ethanol plants are planning to start using corn stover to make cellulosic ethanol, in addition to the ethanol from grain. They plan to use the residue of the stover to create heat. This would do what you say, basically use the corn stalks to cook the ethanol.
Just as you want.
Will it work, I donno, only a couple of pilot plants are being set up now to work out the bugs. You would gather corn, corn stalks. Ferment the corn, ferment the stalks in a different bin. Distill out the ethanol from both using the heat from burning the used up cornstalks. Sell ethanol from both, sell ddg from the corn side, and use the ash from the cornstalk side for a low level fertilizer.