Not at that distance but black hole starship drives are theoretically possible. Far, far beyond our capabilities but possible within known physics. This is like Kardashev type II civilization stuff.
Domesticating fusion would be much easier. That is within sight.
No need for something that exotic. The Earth alone receives more energy from the sun every hour than mankind uses each year.
Yeah but you can't raise trillions of dollars with that. Investors want to be able to tell to their friends at parties that they helped made blackhole tech possible.