I did it in three weeks and I think it's amazing, but many people dislike it. Some give up or stop reviewing, and then they lose it. You really need to use it along with flash cards or, better, an SRS program, otherwise it'll be kind of a waste to do it.
Basically, the only question is about whether or not you think what Heisig does for you will help you. You will be able to write the kanji from seeing an English keyword, and after a while or reviewing, you'll be able to do it the other way around without problem. This works, and people aren't really disputing that.
If you want more proof, here's my Anki graphs (my SRS program I use to review)
When I was starting out:
bayimg - image: anki-stats-2012-11-08@10-06-52.p - free uncensored image hosting
Now:
bayimg - image: anki-stats-2012-12-02@16-12-04.p - free uncensored image hosting
As for the absurdity of the mnemonics: That's a wrong assumption. Many people use mnemonics to remember other things than kanji, but most don't do it with a system. If you want to find out if it's your thing, there's a sample of Heisig's book floating around somewhere. Just google for the remember the kanji sample pdf, you should find it if you look around some.
Now, again, many people argue against Heisig saying that after you're through with it and keep reviewing, you still won't know Japanese. That's very true. Only doing Heisig, you won't know any. But on the other side of that argument are university students who, after five years of study, can write 500 kanji because they used the brute force approach.
As for my personal experience, I love how easy Heisig made learning Japanese for me. I can already read manga without too much trouble (though I've done Tae Kim now as well) and I'm starting to get into the Super Robot Taisen video games, which don't have furigana. That is slow, but it's fun enough to be sustainable. Without Heisig, I'm 100 percent sure I couldn't do this.