Step 1: Understanding the Concept:
Fungi are non-photosynthetic eukaryotic organisms with absorptive nutrition and characteristic storage reserves.
Step 2: Detailed Explanation:
1. Statement I is TRUE: Fungi are completely achlorophyllous and lack chloroplasts, obtaining their organic nutrition heterotrophically as saprophytes, parasites, or mutualistic symbionts via absorptive osmotrophy.
2. Statement II is FALSE: Fungi store carbohydrate energy primarily in the form of glycogen, lipids/oil globules, and the disaccharide trehalose, but never store food as sucrose or starch.
Step 3: Final Answer:
Therefore, Statement I is correct but Statement II is false.