Correct. The laws of quantum mechanics (used for building quantum computers among other things) make very little assumptions on the nature of the universe, and support multiple interpretations, many-worlds being only one of them.

Quantum mechanics is a tool to calculate observable values, and this tool works very successfully without needing to make strong assumptions about the nature of the universe.

I don't know what he's saying, but I'm saying that the answer to your question is "Yes," unless quantum computers behave differently than expected.