Yes, it covers everything the tutorials have and, in fact, a whole lot more. If you go through the book, you will definitely NOT need to go through the C# Crash Course tutorials.
In fact, you can get away with not even reading the whole book. (Though for a book about a programming language, it's not too long, and contains a ton of useful information.) Read the introduction, especially the subsections called "For Busy People" and "For Beginners". They'll point out the sections that are considered "mandatory" and the sections that you can get away with skipping. At least until you get a little further along into XNA game development, or some other larger project like that.
I consider the book to be substantially superior to the tutorials. It covers much more than the C# crash course does, has several parts cleaned up for correctness and others cleaned up for clarity, has more hands on examples to try out, plus quizzes to check to make sure you know what you're doing. I have in my list of plans (which turns out to be a very long list, at the moment) to go back and touch up the tutorials to provide the same level of correctness and clarity, but I've got a handful of other things that are higher priority at the moment. The C# Crash Course will probably never contain anywhere near as much information as my book does, and that's partly because if it did, no one would by the book, but mostly because it has a different goal: a crash course. To get you started as absolutely fast as possible, even at the expense of skipping some useful details. On the other hand, the book is more methodical in covering the fundamentals and how things tie together.
Sorry… that's kind of a long response. Let me know if you have other questions about it!