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,
ESP Ltd B-1005, Fender MP Jaguar, Squier VM Jazz V, Squier VM Fretless P, Mesa Walkabout Scout