Dammit, I stumbled across what looked like a master's or PhD thesis comparing Heisig's approach to others, quantitatively. I didn't read it even though I knew I wanted to. Mental note to find it again.
But if you want to be proficient, you have to be able to read words as a chunk with associated meaning and pronunciation, without the intermediate mnemonic device. So at best it's something you'd want to forget, and at worst it's something that you wouldn't want to learn in the first place.
I'd be totally fascinated to hear about this if you ever find it! I'm greg at memrise dot com.
There's lots of evidence to show that mnemonics boost recollection by a factor or three or so across a wide range of domains, abilities and time ranges. See e.g. http://www.unforgettablelanguages.com/studies.html
Re the intermediate mnemonic device, here's the way I picture things. The mnemonic provides training wheels for your brain, helping you get the answer right a few times. Then, after enough correct responses, mediated by this (hippocampal) mnemonic representation, you rely less and less on the training wheels, and your cortex has had a chance to form a longer-lasting and more direct semantic link.
Disclosure: I'm one of the co-founders of Memrise, so it's not too surprising that I think there's merit in this approach :) Drop me a line or reply here, and I can try and follow up in more detail. Maybe I should write a blog post...
Training wheels is actually a good metaphor, since whether or not one should use training wheels for learning to ride a bike is also fairly hotly debated.
But if you want to be proficient, you have to be able to read words as a chunk with associated meaning and pronunciation, without the intermediate mnemonic device. So at best it's something you'd want to forget, and at worst it's something that you wouldn't want to learn in the first place.