Shouldn't be any problem running the HOB
filter for circulation and the occasional carbon use. I probably wouldn't leave the carbon in all the time. Anything you put in there will eventually become bioactive and start making nitrates.
The theory for the overflow is pretty simple. It's just a siphon. The inside box, set to the water level you want to maintain, fills up. The U tube acts as a siphon to the outside box. As you know, a siphon will equalize levels. The siphon in the overflow trys to equalize the water levels between the two boxes. But, the outside box has a drain into the sump so it can never fill up. Make sense?
I think you'll have better success if your sump is below the main tank instead of beside it. I'm using a similar setup with my 20g tank and a 10g sump...works great. Like fishfreek said, a little overflow maintenance will keep things flowing. I usually just put a bag of carbon in the sump and rely on the flow through the sump instead of running an HOB
filter though. For circulation in your tank, you might look into either the MiniJet or MicroJet PH
's. They are pretty small and will provide good current. I used MaxiJets in my 10, but they took up a lot of room. The LR
and the skimmer is really the only filtration you need.