Energy input during ATP Dephosphorylation?
It sounds like you are asking about the activation energy of the ATP hydrolysis reaction. This paper estimates the activation at 35--39 kcal / mol, depending on details of the reaction mechanism. So yes, energy is needed to break the phosphate bond; this ensures that ATP does break down spontaneously (which would make it a rather useless molecule for cells). 

Note that this concerns ATP hydrolysis without enzymatic catalysis. Enzymes that break the phosphate bond of ATP to drive reactions lower this reaction energy substantially.