Yeah, it's possible to go like that, but really not recommended. At all.
You'll be doubling up both the number of AD/DA conversions (which will give you some signal loss/degredation), and double the amount of space that the project you're working on will take up, as you'll need to be recording everything the mixer outputs.
In the world of analogue tape-to-tape recording, yeah, thats how one would go about things. But with a DAW, thats completely superfluous - sending analogue signal out for mixdown, then recording it back in.
DP (which I use as well) has every control built into the software you'd want to use. If you want physical faders like that, you'll want to pick up something like the behringer control surface (
http://www.behringer.com/BCF2000/index.cfm?lang=ENG), or the Mackie Control Universal (which I'd recommend more, if you have the cash). These are virtual control devices that don't pass any actual audio through them. The DAW version of a keyboard and mouse.
Once the recording is finished on the DAW, and you want to start into mixdown, you want a virtual control surface to give you faders and knobs to control the software values - NOT something that analogue signal is actually passing through (unless it's an outboard signal processor of any kind). This is why you can buy a 64 or 128 track mixing desk for so much cheaper than you'd ever have been able to do previously - because they're control surfaces that get their information from the computer, rather than inputs and outputs.
Does this make sense?