It's not irrelevant. If our economy one thousandth the current size, even a trip to the moon would be difficult. It just wouldn't be producing enough fuel, metal, ceramics and quality human capital necessary for a trip to the moon. It is a lot easier to takes these things from a much larger economy than a small one.
Larger economy can speed up technological advancements too, but I guess that is irrelevant here.
It'll be much more difficult to convince citizens to set up a Mars colony at a cost of $1,000,000 per citizen as opposed to only $1,000 per citizen. Therefore, I'd argue it is relevant. If you were talking about setting up a privately owned colony - a larger economy means there is more chance of a company large enough to take on this task. (In large economies capital is more concentrated, at least that's what I'm observing from history. It would be difficult to have a company the size of Apple in an impoverished country whose GDP per year is less than Apple's quarterly income, for example.)
So every citizen spends $1000 and suddenly you have a Mars colony? No, you have to develop the technology, and that takes time no matter how much money you throw at it. And when you look at the year 2042 and imagine having a Mars colony by then, having an order of magnitude more money rolling around by say 2022 or 2032 won't help if it takes longer than 10-20 years to develop the needed technology.
Larger economy can speed up technological advancements too, but I guess that is irrelevant here.