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Yes. Although you don't need an infinite number of universes. A very large number of years and a very large number of stars will do.

e.g Q: out of billions of stars what is the chance that this discussion takes place at a planet that can support intelligent life?

A: high

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Yes, though there is an important difference between the multiverse approach and the multi-star/multi-year approach. When we imagine the state of affairs in which many universes are created with random parameters, we tend to give those many universes great variety, and we require each one of them (in our imaginations) to be "fruitful" at least in producing a universe. But it's not clear that the mere presence of lots of years (as many as you like) or stars (as many as you like) are fruitful in the same way. To put it back in terms of Joe the die roller, it's as if Joe wakes up most mornings and just lies in bed all day, not rolling the die. Occasionally—one day in a billion—he rolls the die, and it's a trillion-sided die, say. But I suppose the point is the same: the Anthropic principle says that however unlikely conscious minds are, if they do appear (at whatever odds), then... well I'm not sure where to go from there. Then these minds will ask questions about their existence? But that doesn't seem a very remarkable insight.

The anthropic principle goes the other way. It says that if the questions about existence are being asked, then we don't need further explanation of the lucky die roll.

I think the anthropic principle is a response to the claim that that is a remarkable insight.

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