Can xylitol be organic?

How are you intending the use of the word "organic"? On this board, most chemists use the word to mean that the compound is a compound containing carbon. Xylitol is certainly an organic compound in this sense. The other common use of "organic" refers to the ways that foods and nutrients have been produced: that is, without the use of genetic modification, pesticides, and so on that allows them to be certified as "organic". I'm guessing that is how you meant the word to be interpreted in your question.

Most xylitol is produced by the chemical hydrogenation of the sugar xylose. I don't know enough about the rules surrounding labeling a substance as organic, so I don't know whether xylitol produced in that manner from xylose can be labeled as organic unless, perhaps, the xylose itself was originally certified as organic. There is a newer method of producing xylitol that uses a yeast to convert xylose into xylitol. Again, I have no clue whether that product could be labeled as organic or not.

The structural formula of xylitol is CH₂(OH)-CH(OH)-CH(OH)-CH(OH)-CH₂OH.

Xylitol is a carbon-containing compound which is neither a simple oxide nor a simple ion. Hence, xylitol is organic.

'Xylitol ' IS Organic.
Its organic name is 'Pentane-1,2,3,4,5-pentol'.
Its structure is
CH2(OH)CH(OH)CH(OH)CH(OH)CH2(OH)

That is it is a Carbon chain of five carbons (Pentane) with an alcohol (hydroxy) functional group on each carbon.

NB THe word 'Organic' means the chemistry of Carbon , and here we have a five membered carbon chain , so it is definitely ORGANIC.