So in this case, is regular site optimization also important, or can you just rely almost entirely on Adwords?
Welcome to Webmaster world.
the organic search listings are pretty competitive, but there are no Adwords corresponding to my main keyphrase – zero
I'm going to take an slightly different tack here just 'cause that statement seems almost opposed. It's a bit unusual to find phrases that are very competitive in the organic results and not at all in Adwords.
It might turn out that the organic SERPs are not as competitive as it looks at first blush and that a bit of basic SEO will easily bring you to the top. Or, you might have stumbled upon some overlooked Adwords keyphrases that can be mined for gold.
Either way, to me it sounds like a situation where you should work both ends, check the results, tweak and tune, etc. Looks like you have some interesting work ahead of you.
Jim