I'm currently teaching myself MDX for a BI project at work. I spent about 20 hours reading through the Practical MDX Queries book (which is very good by the way) and applying the lessons against my cube (not Adventure Works). At that point I felt I could do the basics but still had to reference the book frequently for some specifics.

I've probably spent 50 hours writing MDX queries now and am starting to feel comfortable with the language.

Based on my experience you can pick up enough to be minimally functional in 20 hours but definitely need more time to become competent.