This proposition is true if at least some possible computations (not necessarily any that could run on modern computers) have consciousness, sapience, or whatever other properties are necessary to make them people and therefore objects of ethical value.
Key argument: Most domain experts think that human beings are themselves (a) Turing-computable and (b) conscious in virtue of the computations that they perform. In other words, you yourself are a conscious algorithm. If you consider yourself a person, then you consider at least one computer program (yourself) to be a person.
This is why some domain experts can be very confident of the proposition, despite the moral subquestions about which properties are necessary for personhood. If you take for granted the Church-Turing thesis stating that everything in the physical universe is computable and therefore so are human beings, then of course some computer programs (like you) can be people or have any other properties we associate with human beings.
This proposition falls into the class of issues that some people think are incredibly deep and fraught philosophical questions, and that other people think are incredibly deep philosophical questions that happen to have clear, known answers.