BUT! You will not be able to read Japanese. He explicitly states that you shouldn't learn the readings until you can write them. All 2000 odd of them. The second book teaches the readings, completely out of context as a list of arbitrary vocabulary.
Now, I don't think that working through the Heisig books is a waste of time. On the contrary, it's a good as way as any of familiarising yourself with Kanji. The first Heisig book is a very well defined project, in project management terms. It's got a measurable goal (number of kanji covered), a definite end (the last page) and clearly definition of success (being able to write the kanji and know one English meaning).
The problem I have with Hesig is the way he recommends going about the challenge. If you really want to extract any sort of enjoyment from learning kanji and get through it as quickly, superficially and joylessly as possible, then Heisig is as good a method as any. I've seen an estimate of about nine months to work through the books. That's nine months of no reading, only learning how to write the Joyo kanji and a single English meaning.
You don't need to know 2000+ kanji before you start to read
There's a reason that Japanese children learn the Kanji in stages: there's no point learning kanji for words you don't know. The 1000 kyoiku kanji taught in primary schools are, mostly, fairly practical kanji that you see a lot. Once you go above that, though, you need to have a fairly decent vocabulary, and by the time you get to the end of the Joyo kanji, even Japanese people will say they've never seen the characters before. These are extreme examples, but 璽 'imperial seal' and 朕 'first person pronoun for the emperor' are not everyday words. Even in the Kyoiku kanji, do you really need to know 后, 'empress'? I see 壺 tsubo 'jar, pot' a lot more and it's not even a Joyo kanji. Why would you need to know these when you're not yet reading the language?
Not only that, but the more kanji you know, the better you get at remembering them. It becomes easier to remember them as made up of other kanji, rather than as stories in English. By the time you get to about 500-1000 characters, you've probably outgrown the need to create a story for every new kanji. I had a look at book 3 (now out of print) for learning the 1000 kanji beyond the Joyo. I got about two pages in before it became clear that it would only be useful as a list of relatively frequent kanji. In the first couple of pages it gives the mnemonic for the element 粦 as 'shoeshine', which it states is an arbitrary name for it. Now, if you're onto your third thousand of kanji, there are at least ten better ways of remembering it, especially when you consider that you should already know the kanji 隣 very well indeed by that point.
Learning kanji without readings actually makes learning them harder
The kanji 責 is in 積 and 績, and they all have the Chinese on-reading of seki. This is not a coincidence. If you learn that 責 is read seki (in the very common word 責任 sekinin 'responsibility') then you've learnt a reading of the other two. However, when writing the kanji 積, you may remember that it has the reading seki, reinforcing the right hand side being 責. This circular logic may seem counterintuitive, but eventually it becomes clearer how the 'sound' part of kanji works, and how 青, which usually has the on-reading of sei, could give 情 the reading of jou. I have often surprised myself that I remember how to read a kanji just by looking at it, even though I don't really know the character. The brain works better if you reinforce knowledge in many different ways, and it can make connections even without you being directly aware of it happening. Admittedly, the second Heisig books tries to teach the meanings in this way, but why wait until then before you can make that connection?
Heisig only teaches one (sometimes irrelevant) meaning
Knowing the English meaning of a kanji is a good way of understanding it, but limiting yourself to a single word doesn't make sense. Many kanji have a very broad meaning to begin with, but Heisig often choses a fairly esoteric and rare meaning as his key word.
For example, in the video below, Chris Broad explains how he learnt the character 摂 using Heisig.
I have two problems with this. The main one being the key word 'surrogate'. My Kanji dictionary lists 'act as an agent' as the third meaning, and the two example words it gives with this meaning are so rare that they're not even in a medium sized Japanese dictionary. In most words, the character has the meaning 'take' or 'take hold'. The second point is that in the context of Japanese, this character doesn't need the convoluted explanation given in the video. 摂 appears in the word 摂取, sessyu 'intake (of food or nutrients)'. 取 means 'take', as it's a hand 又 taking an ear 耳, and originally meant cutting off an enemy's ear. The four dashes mean 'the above repeated twice', so it's a hand 扌taking three ears 聶, i.e. not just taking, but really taking in. So now I've learnt an example word, related it to a similar meaning kanji, have a mnemonic for how to write it and know the reading.
Even for simpler characters it doesn't make sense to only learn a single meaning. 日 can mean day, sun or Japan. These are all elementary meanings and there is no need to restrict yourself to only one of them.
You will forget some kanji however you learn them. And that's fine.
This review of Heisg seems to suggest that you will never forget Kanji learnt through Heisig's method. I say to that: rubbish. It also mentions the myth that Japanese children only learn Kanji through rote learning. Again, nonsense. Yes, they do write them out a few times when they first learn them, but after that it's practice through writing essays, reading books and seeing the characters in context. Japanese people use kanji every day of their lives, and yet still forget how to write them. Knowing Heisig's mnemonics is not going to prevent that from happening. Twenty years down the line, Kanji will feel like second nature to you, but you'll still forget exactly how to write a kanji sometimes. This is just the brain being efficient, but learning and forgetting is not the same as never having learnt in the first place.
Working through Heisig is going to give you a better understanding of Kanji than having no knowledge at all. It doesn't give a deep understanding of kanji, and it doesn't allow you to read Japanese. So while it may achieve what it sets out to do, that aim isn't to speak or understand Japanese. The only way I can see that being the best strategy is if you're not in Japan and aren't taking a holistic approach to learning the language. Even then, you're going to need a lot of patience to stick at it. It does provide a list of read-to-use mnemonics, but if you really haven't got the imagination to come up with your own, I'd recommend Henshall's 'A Guide to Remembering Japanese Characters' over Heisig.
To answer the original question: is Heisig effective for learning kanji? It's effective for learning kanji in the very narrow definition of 'learn' that Heisig uses. But you'll still be a very, very long way from mastering them or even reading Japanese. Do it if you want to, rave about it if you like, but it's not magic, and it still takes a huge time commitment and a lorry load of perseverance.