Should be the same latency that you get when working with your own DAW. It's just translating your system's internal audio APIs (so for me on Mac, it's Core Audio) into something that can be used on the Web with JS.

The Web Audio API is pretty awesome. I've been trying to pair up with some folks to see if we can build some kind of web DJ software. Imagine being able to JIT download songs from Spotify, Soundcloud and Youtube and DJ with them :)