I am not sure whether what I write below is in line with Corum's views or not, as I don't spend a lot of time on conjoined predications. I am simply trying to explain why in answer to your original question, my answer was, 'It's a matter of personal preference". I should have added, "with this utterance".
If your original sentence had been
"These predictions will be purely informal, will have no binding character, and will leave X free to do as he pleases",
then will cannot be omitted. This is because 'have' and 'leave' could be interpreted as present simple forms in the version without will.
However, in your original:
"These predictions will be purely informal, will have no binding character, and will not oblige X to place orders",
omission of will leaves have and not oblige. Not oblige is not possible as a present simple form and is appropriate only if the omitted will is understood. It is therefore natural to assume that have is also dependent on an omitted will.