Consultancy projects either create significantly more value than their project cost or they don't. If they do, then they are worthwhile for an organisation to commission. This equation should be uneffected by the state of the economy (though the nature of the projects will change as what creates value will change in different parts of the economic cycle).
This is the rational way of thinking about it. In reality, some companies may panic and cancel projects if they think the economy may go downhill, but that's a small and temporary thing.