Mr. Hobbs - we really need more data to determine why that recommendation was made. However, my guess is they are suggesting the mixer for getting the audio into the computer to begin with, rather than for mixing after it's already in the computer.
To capture voices (and other accoustic instruments) you will need microphones. Mics can not be connected directly into your computer's sound card, and they need a signal boost first (pre-amplification). You can buy standalone pre-amps for this, but generally a more economical and more flexible approach is to use a mixer.
To answer your question - yes, you can mixdown on your PC, and generally that would be the recommended way to do it. Mixing on the PC allows you to keep the signal in a digital state, rather than go through a D/A conversion if you go external to a mixer (and then another A/D conversion if you dump to CD).
So my guess is they were suggesting the mixer for the recording phase of your work.
