Coming in late, but better late than never, right? I maintain LinkedIn just as an online presence, a place for people with whom I've already "linked" elsewhere to check me out. It does its job for that.
Some groups might be useful to join; I've seen job postings in a few I belong to. Mostly the groups are social and question/answer outlets, though, and there are far more people who don't know anything than people who do. I withdrew from one writers group after seeing the umpteenth reference to the shitty ol' Preditors and Editors site. None of the writers groups that I belonged to were worth much, IMO. I sent join requests to one or two others but never got a response. Maybe that's where all the bigshots hang out. lol
Spam isn't taken lightly by a well-run group. The terrible groups are terrible because they allow so much self-promotion (and this spans multiple types of groups, such as investing and real estate). The good ones kick self-promoters out. So I wouldn't approach LinkedIn with the intent of advertising your book. Unless the moderator has a specific board for it -a spam board that no one clicks on except to advertise their book. I don't know why the posters think anyone else would read the board when even they don't.