I also shoot the D7000 and I use shutter priority for sports action shots. Aperture, while you may think 5.6, 8 or 11 is going to give you great depth of field, the camera is going to assess a shutter value commiserate to said number and you are going to have more blurs than tight, clean shots. If you are really-really-really good at panning, you might get away with aperture priority. Flash in an indoor arena big enough to accomodate a rowing competition, I suspect is going to be a moot accessory....then again, not knowing what the facility looks like, I cannot really judge this as an absoute. The 18-105 is a not a terribly slow lens on the wide open side of lens, but a dog on the other end. Do you have a faster lens?
By the by, you can adequately shoot the D7000 at ISO 2500-3200 with reasonable noise and that noise can be pretty reasonably compensated for in your Camera Raw editor. There are others on here who have far more experience in shooting this type of venue, and I would give their answers far more credence than mine, but that said, I have been shooting the D7000 since it first came out as I was one of the fortunate first few to get one straight away. I know the camera and I know the lens and I know from the getgo, you are probably going to have to get a faster one, or use shutter priority set to 1/1250 or thereabouts to get as close to the results you want as you can get.