Welcome back.  That's a great question.

It's kind of an apples and oranges thing.  First:  Apples.  You can learn Heisig's (or any other dictionary's) 2000+ keywords in a reasonable amount of time.  It'll probably take you a few months, and they'll be somewhat useful.  They'll help provide you with some context for the things you read, although you won't be able to actually read.  Where they really help is in the next learning phase, which is understanding vocabulary.  So instead of thinking of "chikuwa" as just something floating in your oden, you'll be like, "Oh, it's 竹輪, a BAMBOO and WHEEL-shaped thing," floating in my oden.  And then it tastes better, maybe.

Bottom line is you'll still need to learn a ton of vocabulary, but the keywords will help you make some sense of them.

Okay, now Oranges.  This approach is working from vocabulary backwards.  The advantage to this method is, as you mentioned, that you're learning words in actual context, and (presumably) learning phrases that are actually useful to you.  You're also (again, presumably) learning pronunciations, which is, um, kind of useful in that you can actually speak words.  RTK can be rather academic, in that you can just geek out on learning a ton of kanji and forget that there are actual Japanese people to talk to.  On the other hand, the drawback to not studying RTK first is that you'll be all over the place.  You'll see the word 車輪 and think, "Hey, I saw that kanji before.  But what the heck does it mean?"

I questioned Heisig on this point a couple of years ago, and he said that was his entire point behind learning the kanji independent of their readings:  they provide a way to make sense of the words you encounter.  Without that, you're just trying to keep track of random symbols without meaning (even if the meaning of the keywords are overly constrained).

You'll probably get lots of other opinions on this, but mine is that I'd do (and I did) both Apples and Oranges at the same time.  I made two Anki decks and worked them both simultaneously.  One deck had kanji and keywords, and the other deck had useful sentences.  When the two eventually intersect, you'll have a good understanding of the words in context.

It's slower to learn two decks rather than one, but I felt it was valuable because I was able to immediately apply what I learned to real life.  If I had a problem with my landlord, I was like, "What the heck's "landlord" in Japanese anyway?" and then I'd enter that word into my Anki "Useful Sentences" deck.  (Always as a sentence, by the way, rather than as an individual word.) 

Hope that helps a bit.  Sorry for the long reply.

Ken

You want to be going: see a japanese word -> sound and meaning. The keywords only give you half of that and it's usually not that accurate. Meaning you're going to have to be doing a lot of dictionary lookups anyway and/or getting meaning from translations, and the pronunciation from audio or furigana or guesswork. The keywords may act as hints that help you identify some of your earliest vocabulary but really you'd get the same effect from just learning japanese words. The thing to take away from RTK is some idea of the radical meanings, writing ability and exposure to the Jouyou set.

Thanks for all your helpful answers.