If you are thinking about a combined production of sugar and ethanol, then the amount of crystalized sugar influence the production of ethanol. In this kind of industrial plant, the sugarcane juice is usually diverted to the sugar production and only the part that is not crystalized is used for ethanol production.
If you want a maximum production of ethanol, you can use all sugarcane juice for ethanol production and, in that case, you will not produce any sugar. This kind of industrial plant is called autonomous distillery.
I am giving tis with the prospective of production of ethanol for fuel application
Producing crystallized sugar and then making ethanol will be inefficient in terms of amount of total ethanol fuel yield irrespective of quantity generated. Cause you are using additional energy/ fuel for obtaining crystallized sugar. So net energy is less.
Best way would be , as Furlan said,
Proceed for autonomous distillery and get maximum ethanol fuel per kilo of sugar cane
Depends if you want to do it in the Lab or on the ethanol plant itself.
See this experiment which you may modify to suite your conditions.
Samples of beet were collected from Nyandarua Sugar factory and small portions of each were perforated. The mixture was fermented. After fermentation, each portion was filtered and the filtrate distilled once. The alcohol content of each of the distillates was determined by use of analytical techniques. One litre of fermented juice becomes the precursor of fermentation in a 50 liter can of fresh juice. But for fresh juice, you may need about 100g of Yeast.
Sugar Beet juice to Ethanol conversion ratio (kgs/l) is approx 6:1
Distillation of a 50 liter can takes about 2 hrs when boiling in a pot. A pipe is connected to a pot passing through another pot of cold water into the pure ethanol receiver vessel. This will give about 5 liter conc. ethanol.
There is need to conduct some experiments to verify this but the following is my take.
Sugar is Sucrose. If you have white crystallized sugar it does contains 99.9% sucrose. Therefore the ethanol yield will be slightly higher. Raw sugar from cane may contain colorants/enzymes which will affect fermentation resulting in lower amount of ethanol produced.