The introduction to Kanji ABC outlines two methods for using the book: (a) alternate between learning a dozen or so graphemes and then the characters which are made with those elements, or (b) learn all 500 or so graphemes first, then approach the kanji in whatever order you desire. I have tried both of these paths and would like to relate my experiences:

For the first 300 or so kanji I took path (a). I felt that this more closely matched the approach of Heisig, and at the time I didn’t see any reason to deviate from that path. But then I began to get impatient about starting Chinese characters and my 10,000 Japanese sentences, both of which would require learning some of the frequently used, but complex characters found at the end of Kanji ABC [a bad idea, but for reasons I’ll explain some other time]. So I put my Kanji input on hold and started adding just graphemes to my SRS.

This worked… for a while. But the more I advanced in my grapheme-only studies, the more trouble I had learning and retaining that knowledge. By the very end I had come up against a wall. I was forgetting the writing of graphemes just as quickly as I was adding them. In retrospect the reason was clear: unlike kanji, the graphemes have no mnemonic components, so frequent use is the only reliable way to remember them. And by neglecting my kanji studies I was never using the graphemes. In essence I learned the 500 graphemes following the traditional rote method for learning the kanji, in less than a month. That itself is pretty incredible, but hardly efficient (I could have learned twice as many kanji in the same period of time at the rate I was progressing). Taking this approach was extremely aggravating, and probably added 2 weeks to my kanji studies. I would not recommend this approach.

Conclusion: study graphemes and kanji simultaneously. It is more efficient, less frustrating, and will speed you towards your goal of complete mastery of the kanji.