if you add something organic, like glucose, to water then technically the glass of sugar water is now "organic" because of the presence of the organic sugar. The H20 molecules themselves are still inorganic, but the organic glucose molecules are present and mixing around with them. It's technically a mixed compound with both organic and inorganic molecules.

https://www.sciencedirect.com/topics/medicine-and-dentistry/glucose#%3A%7E%3Atext=Glucose+is+an+organic+compound%2Cof+hydrogen%2C+carbon+and+oxygen.&text=It+was+first+discovered+by%2Ca+German+Scientist%2C+in+1747.&text=It+is+classified+as+a%2Calso+referred+to+as+dextrose.

As to your question, if you somehow altered the H20 molecules to include carbon in their molecular chain, they would cease to be water and would become something different. If you just add organic molecules into a mixture with water, then it's just a mixed compound.