Of course they can do it. I just dont think is a clever move for them to do it.
Firefox is having a hard time to compete with Chrome, and they took too long pursuing other goals, and just remembering one key feature they took a lot of time to implement, was making Firefox a the multi-process browser as Chrome.
I mean, you would be ditching all this effort, rewriting it in Rust, spending key resources only to have some parity with the same browser you already had in C++, spending years, and loosing more market share, as Chrome can spend this time in optimization and features.
For the record, i think Rust is what will save Mozilla, but it must reinvent itself. Do the best they can with the firefox codebase they have, and use Rust for new projects.
Like, creating Cloud, backend system software, and reinvent itself like Ubuntu is doing right now.
They have to be very strategic and pragmatic right now. Two big moonshots, Firefox OS and Rust, and only one of them has paid out their time and resources.
If they want to bet in more moonshots, great, but they must do it in "blue ocean" places, being more innovative on where they should use Rust, were Rust can shine.
I just think that from a strategic (and even technical) point of view, they are just spending precious resources, while at the same time eroding even more their browser market share.