There are people with naturally high metabolisms who are underweight but are still healthy because they are consuming enough for their bodies. But they were built to be underweight. They are not depriving their bodies of anything. Most people cannot be naturally underweight and be healthy as well. To be underweight they have to consume less food than their body needs.
It depends on what you mean with underweight. In terms of body fat percentage, no. You can live healthy, but it isn't going to prevent the horrible damage to your body such as loss of bone density, often anemia etc.
If you go according to your BMI, yes, you get people who are underweight in those terms but live healthy.