Will electric field make organic matters (e.g. glucose) ionize in water?
The short answer to your question is no, particularly for your example of glucose. Part of the key to your question is the statement: "[...] will the electric field ionize the organic matters that are not ionizable?".  If they are not ionizable, then they are not ionizable :)  

You could electrolyze glucose to polyhydric alcohols as in this patent. But in this case you are not ionizing glucose, but creating an entirely different compound (which is still not strongly ionic).

There are compounds that can be electrolyzed to ionic compounds, but that is really a very different process than what you are asking about.  You wouldn't have ionization of the compound, you would be electrochemically converting a non-ionic compound into an ionic compound. See for example, this abstract1 in which the authors electrolyze ethanol to acetic acid, which would then ionize in the aqueous solution to some degree. 

But, as in your example of gucose, the ethanol itself would not be ionized. You would simply be producing, via electrochemical reaction, an entirely different, ionic compound.

1) Journal of the Electrochemical Society, "Electrolytic Oxidation of Ethyl Alcohol to Acetic Acid", 1947, volume 92, issue 1, 335-342