To answer your question, yes. It can get low enough. My action is actually really good.
But what I don't remember, is if I shimmed the neck or not. I'm pretty certain I put about a 1/2" wide strip of business card at the end of the pocket toward the bridge, I don't have a problem with shimming the neck (if it's okay from the factory, it's okay with me).
All the best,
SBMM Ray35, Ibanez ATK300, Fender Modern Playa Jaguar, Squier VM Jazz V, Mesa Walkabout Scout