The focus motor is a standard gear type. As @MarcinWolny said, this is used on all DSLRs that have an AF motor.

You are right that the sound-track of videos will be ruined if it records the AF noise. But what you do not know is that Contrast-Detect AF will ruin the video track. This system needs back-and-forth movement of the lens to lock focus and this is visible in videos. You also run the risk of the camera focusing on the wrong subject.

Unlike with still photography where missed focus happens between shots, a video records every attempted and missed focus the camera does. Quality videos are done with manual focus for these reasons. So, in other words, the point of how much noise the AF system makes is moot.

Contrary to popular belief, ultra-sonic lenses still make noise. Some more, some less, but they still do and it can get recorded in the audio track. If you are shooting a vista without sounds for example, you will often hear the hum of the ultra-sonic motor. If you shoot a busy scene with people talking and music though, you are unlikely to hear it.

Should you insist to use autofocus for videos, you should either get an external microphone which the D7000 supports or an external audio recording device and synchronize sound by software later. There are plenty of external microphone available, some mount on the hot-shoe (Nikon makes one of these) and some are even wireless.