You are asking two different questions here. The main question asks about “truly happy people” and whether they are unambitious. But the question in the details asked about “people with low ambitions” and whether they are happy.

That’s like the difference between the questions: “Do all dogs have ears?” and “Is everything that has ears a dog?”

While I can’t answer the question about unambitious people, I can at least partially answer the question about happy people…because I am one. And no, not all truly happy people are unambitious, because I’m an example that proves the negative: I’m truly happy, and relatively ambitious.