Pff... You leave your thread alone for a week or so and look what riff-raff walks in... (Hullo!).
In answer to your question, yes and no...
The story is told through the eyes of a different character than the original, which allows Baxter to side-step having to replicate Wells writing style exactly. That works well for the most part, but it falls over when he drops in phrases/lines from the original novel not as quotes - because the original book is a published work within this story - but as part of the new character's narration. I found it rather jarring, to be honest, and a bit of an odd way of invoking the feel of the original (which I don't think this book does very well).
Overall, I wasn't that taken with the book. It suffers from the same kind of escalation that very few sequels manage to carry off (to my mind this is more Independence Day 2 than Aliens, although that may be a bit of a harsh parallel to draw!). It's certainly from the "More is better!" school of story telling. Also, the way the narrator is kept at the center of the story is terribly contrived, and the book takes forever to get going.
There are some good ideas in the book though, and the use of contemporary real life people (such as Churchill) is interesting. I also liked a section where events are told through the eyes of several different people around the world, but it's all too patchy and feels like a bag of ideas loosely held together by the main narrative.
I re-read War of the Worlds in preparation for reading this and where Well's original is concise and beautifully written, this is almost the exact opposite.
I did write up a review when I finished it, but wasn't happy with it so I didn't post it. Perhaps I should look at it again and have another go, but the above pretty much sums up my feelings about the book. If I were being charitable, I'd give it 3/5, and wouldn't really go out of my way to recommend it (my sister loved it, however, but she married a Scotsman and lives in Wales so, like, how good is her judgement?).