It should be able to... Hopefully Go and Java will be some of the first GC languages to target WASM, and we'll find out :) . Personally I'm more worried about the size of the GC getting added to the binaries than how fast it is.
AssemblyScript already does it, if I am not mistaken.
If the Javascript garbage collecter can do it then I don't see why not.
The JS GC can run in native code, in a separate native thread with shared memory access, and it can use things like memory barrier instructions, which have no equivalent in WASM yet.