Whether zero-calorie or diet drinks belong in a fast or a deficit is a common question, and the honest answer is that it depends on you. They help some people a great deal and work against others, so rather than a verdict, what helps is a way to find out which group you are in.
What they do when they work
For the people they suit, these drinks do two jobs. The first is taste and texture: when you want something sweet or cold, a zero-calorie drink gives you that without the calories, and the craving often passes. The second is more about habit than hunger. When your head wants a small break and reaches for something, a drink with some flavour fills that gap where a snack used to go. Used that way they take real pressure off the strict stretches, which is when most attempts come undone.
The honest qualifier
They are not free of downside for everyone. Some people find that the sweetness, even without sugar, leaves them hungrier rather than steadier. Others find these drinks disturb their sleep if they have them later in the day, often because of the caffeine in colas. Neither effect is universal, and plenty of people get all of the upside with none of it, but you cannot assume in advance which one you are.
How to test on yourself
This is what the warm-up phase is for: low-stakes experiments before the real work begins. Have these drinks for a few days and pay attention to two things. Do you end up hungrier an hour later, or calmer and steadier. Does your sleep get worse on the days you have them, especially in the afternoon and evening. If they help, you have a genuine tool for the hard stretches ahead. If they work against you, you have learned that cheaply, now, instead of in the middle of the program when you can least afford the surprise.