Based on the way this question is phrased, the answer is trivially no. No matter how you make an ATP molecule, if you measure hydrolysis in a consistent manner there will be no difference.
A fundamental axiom in chemistry is that identical molecules are indistinguishable from each other. Specifically, I mean that the entropy and enthalpy are State Functions - they only depend on the current state of the system and not how the system got there. This is best summed up with Hess' Law.
The only things that could change the free energy of hydrolysis of an ATP molecule are:
- A change in the isotopic makeup of the ATP molecule
- A change in the environment in which the hydrolysis is occuring
The first is very, very unlikely to be dependent on aerobic vs. anaerobic respiration. I mean I guess the isotopic makeup of the oxygen could be ever-so-slightly different or something, but I would be shocked if it was. Even then it almost certainly wouldn't make much of a difference in energy of hydrolysis.
The second, is actually very likely to occur. Changes in temperature will always affect any reaction for which the change in entropy is non-negligible (remember $ \Delta G = \Delta H - T \Delta S $). As you suggest, changes in pH would certainly effect a measured change in energy due to a change in the abundance of the various protonated forms of ATP (and keep in mind hydronium if you're considering spontaneous hydrolysis). Indeed, almost any change in the environment could affect the measured energy.
But, importantly, these are not due to differences in the actual ATP molecule. These are due to differences in the environment that the reaction is taking place in, not the environment it was produced in. If you take two ATP molecules and place them in an identical environment they will always have the same energies (isotopic differences excluded). Any evidence contradicting this is either wrong or a suggestion of a fundamental paradigm shift upending years of basic physics and chemistry.