What your trying to do is not impossible, but it will take quite a few channels. We had this setup in college. We used a 32 track board and heres how we did it. The sound comes into the preamp on the board, through the board, then out the direct out on each individual channel. Your board has to have direct outs for this to work, not all do. Then the source goes into your sound card, the analog to digital conversion happens here. Then into your computer, through its processing, then you can assign it and out, say out one. So you have 16 channels comming into the board and into your firepod, 002 or whatever will accept 16 channels. Then you assign the outs of the individual channels in your DAW to corespond with inputs on the mixer. You used the first 16 channels as ins, now your using 17-32 as outs 1-16 in your DAW. The sound goes out of the sound card, does its digital to analog conversion here, then you can basicall mix on channels 17-32. Then the sound source goes to your main outs, at this point it is captured by your media, whether it be a tape machine or back into your DAW. This is basically using the same mixer for tracking and summing/mixing.
As someone said before, unless you have a big fantastic sounding mixer you wanna avoid this many Analog to digital and digital to analog conversions. I just use my mixer as a slave, using the pres and eqs on the way into my pro tools. I dont mix on my mixer, but unless your board has automation its rather pointless to mix on. If you dont have a bunch of outboard gear this is rather pointless as well. You can benefit from the analog summing, but if the mixer is just so so the benefits will be cancelled out cuz of all the conversions.
What someone suggested is just a midi controller. This does not have outs and will only complete the second half of the equation. It will control your DAW. While this is nice, it has not bearing on the audio.