Adat is a digital 8 track recording machine that uses digital (vcr) tape as its media. It has 8 analog ins and outs, as well as a digital in/out that can be hooked up to a pc. The digital in/out requires a soundcard with a "lightpipe" function in order to make a transfer from adat to pc completely within the digital domain. The adat also has sync locking features that allow you to combine two or more adats for 16 or more tracks, or even a sync between pc and adat. It also has basic digital editing features such as track copy, delay, and pitch change. It also has a great punch in feature.
So yes, you can sync up a pc with an adat, giving you more tracks.
I do not know how an adat works in conjunction with standalone recorders, but I imagine it depends on the particular harddrive recorder you are using. Product specs will indicate whether a particular piece of recording gear is compatible with Adat. You would need a mixer if you were mixing from Adat down to a standalone recorder.
But if you have a pc, there isn't much of a reason to go out and buy a digital mixer (unless you really like to play with the knobs) Most people with an Adat/pc setup will use an analog mixer only to capture a warmer sound quality that is said to be absent from a full digital setup. But if you are getting a digital mixer, what's the point? You might as well save some money and mix in the pc.