I don't actually have volume 2, but I bought volume 1 for self study and gave up on using it for that when I was still a beginner. However, at the time I only had paper dictionaries to work with.

It still might have been workable if I'd been more patient; I did go back and read it through as an intermediate student and picked up some new things that I hadn't from Japanese for Everyone and Tae Kim's Guide, and some new perspectives on things I already knew a little about.

Anyway, if you realize you are going to be faced with kanji for which you don't have the readings and are prepared to look up your vocabulary it's still a useful book. You can get a lot of the readings (for anything in the dialogues) by flipping to the romaji transcripts at the end of the chapter, but example sentences don't limit themselves to vocabulary in the dialogues so you will be looking up kanji. (jisho.org's character lookup by radical works well enough if you don't have a good way to input by writing the character with mouse or touchpad, although I would use yahoo.jp's dictionaries in preference to edict, assuming you don't have your own dictionaries.)

I have books one and two; I finished it maybe 3~ years ago, so here my 2 pence...
You really do need book 2, only because it gives you a chance to practice what you learn in book 1. Book 2 is basically an exercise and vocab book. The vocab bit isn't really all that important as you can use a dictionary, and anki anything that you don't know.
As for its difficulty: I got the set a few months into learning Japanese, and I found it to be hard; very hard. There are no answers to the exercises, and the pacing is incredibly fast. That said, it wouldn't have been anywhere near as difficult if I had someone to check my exercises and offer advice. What's more, I didn't have any other books or resources to draw on like the times grammar dictionaries, or really anything else for that matter. Not to mention I pretty much went from Gilhooley's Teach Yourself Beginner's Japanese to these books.

tl;dr
You should get them as a set of 2. How difficult it is depends on what level you start at, what other books you have, and whether you know anyone who can offer advice and check your work.

Can't say I enjoyed doing this series at the time, but I'm glad I did; I really learned a lot.

I assume you mean "Introduction to Modern Japanese" by Bowring & Laurie? I think there's also a different book by different authors, but with the same name...

I used these books to get started with Japanese. The learning curve is not that bad once you get rolling, and halfway through you have enough stuff under your belt to start tackling some native material (although very slowly at first --- I started reading 精霊の守り人, and finishing the book took me half a year...).

The workbook is indeed almost necessary, as it contains the vocabulary lists. The romaji transcripts at the end of the chapters were IMHO pretty useless, flipping pages back and forth gets old fast.

Good points for this series:

+ Immediately uses the full writing system (some kanji in the first text you see, no furigana).
+ Good explanations of the basic grammar points, concise and to the point.
+ The approach of studying well-explained written text that get progressively more difficult works well for self-study.

Bad points:

- The workbook was pretty useless for me, apart from the vocab lists. The exercises get boring really fast, and since there's no answer key, you'll have to find the answers otherwise.
- A bit expensive. (OTOH, you do get 52 chapters, which will keep you busy for a long time.)

I don't know how this compares to Genki or some other popular book series, as I've never seen those. However, I liked that it pulls no punches and does not try talk down to you.