Rely on live rock for biological filtration and skimmer to catch particles/charged compounds. I still highly recommend the use of carbon to remove refractory compounds that are not removed via skimming nor are they removed often enough via water changes. At the very least, it keeps the water from becoming tinted (which is often difficult to see, unless there is a side-by-side comparison). I have never seen any issues stemming from extended and continuous carbon use (unlike the overuse of GFO). Since we don't really know all of the compounds that sprout up in our tanks, it is difficult to make a blanket statement, I suppose. However, in general, these levels do often accumulate to much higher than typical seawater levels (especially in tanks with a less-efficient skimmer)--by bacterial metabolism and coral/cnidarian byproducts, etc. From what I've seen, the accumulation of organics has less benefits to offer than detriments. You can read up more on organics here.
To be honest, this is the first I have ever heard of cycling a tank with no filtration.
To be honest, this is the first I have ever heard of cycling a tank with no filtration.