If Nutrition Facts states 0% Cholesterol does that imply the food is vegan?
Your question implies that cholesterol only comes from animal products. This is not correct. Cholesterol is present in many plants. 

Other answers and comments claim that only amounts "less than 0.5" (units omitted) of cholesterol is permitted to be listed as 0, and that "no cholesterol" is an added claim that a product is truly cholesterol free. This too is incorrect. The FDA permits amounts less than 2mg/serving to be listed as both 0 and "cholesterol free". There are additional caveats which can be read at the link.

The bottom line is, not only does 0 mg of cholesterol not indicate anything regarding the presence of animal products, but neither does the presence of cholesterol.