Servo contributor here: Haven't heard of this plan (still could exist), though we do (mostly jokingly) toss the idea around every now and then. There are a couple of not-production-ready Rust JS interpreters floating around (https://github.com/swgillespie/rjs/ is the latest I've seen) though.
Stuff like JITs can't really reap Rust's safety+performance benefits[1], and overall the same might be said of a JS interpreter, with all the garbage collection and stuff. The other thing is that Spidermonkey/Chakra/V8 have had years of optimization and tweaks, starting from a clean slate would be _very_ hard. With Servo's small team this is an impossible task, but with a larger, dedicated, team, there's a chance. shrugs
[1]: though it's possible they will still be safer than the C++ counterparts, which is still good. The question then becomes, how much is that increase in safety, and can it justify a whole rewrite?