Unlike SpiderMonkey, V8 doesn't have a special mode for "use asm" code, as far as I know. E.g. it still does JIT compilation, unlike SpiderMonkey, which does AOT compilation.
But the V8 team is certainly working on making asm.js code fast. This is clear from the fact that V8's performance on asm.js benchmarks has increased significantly since asm.js was first announced. (As you note, they put an asm.js test in their own benchmark suite.)
And even if V8 doesn't have a special mode for asm.js, they're benefitting from asm.js's existence, because asm.js makes clear exactly which subset of JavaScript they need to be optimizing for.
V8 has an experimental new JIT called "TurboFan". AFAIK, it doesn't do AOT compilation of asm.js code, but the "use asm" directive (among other cases) will force TurboFan mode.
Unlike SpiderMonkey, V8 doesn't have a special mode for "use asm" code, as far as I know. E.g. it still does JIT compilation, unlike SpiderMonkey, which does AOT compilation.
But the V8 team is certainly working on making asm.js code fast. This is clear from the fact that V8's performance on asm.js benchmarks has increased significantly since asm.js was first announced. (As you note, they put an asm.js test in their own benchmark suite.)
And even if V8 doesn't have a special mode for asm.js, they're benefitting from asm.js's existence, because asm.js makes clear exactly which subset of JavaScript they need to be optimizing for.