It appears that most people now mix in the box these days, and for some good reasons. So, before you go though the effort to do this, you may want to consider some things, such as the differences. I'm not trying to sway you, just offering some things to think about.
When you work all in the box, saving your project saves everything, including your mix, automation, plug-ins, virtual instruments, etc. Mixing through the mixer means that you'll need to save your mix settings on your compact flash card or on your computer via TMCompanion. So, you'll need to name your files for each song so you can easily restore computer and mixer settings if you later return to a mix.
Also, the DM is a digital mixer, so while it may feel analog, you'll still be mixing in the digital domain just like you would be "in the box". It'd be different if you were mixing in a great sounding Neve, SSL, or some such analog mixer or one with an analog signal chain that would impart some of its own signal changing characteristics.
That said, there are some signal changing characteristics imparted by the A/D and D/A conversion process each time you go back and forth, but these are not generally considered changes that improve the sound. You don't say whether you'll be converting out of the box and going into the DM line inputs and mic pres in analog, or transferring the tracks in the digital domain, such as via Firewire, but you should at least be aware of what you'll be doing.
You mentioned not using any plug-ins, but not whether that means no signal processing, or that you intend to use the mixer's EQ, compression, limiters, effects, etc., or outboard gear, or actually no processing. But if you'll be using the mixer's effects, they're digital, just like plug-ins. And if you use outboard gear, unless it's truly analog gear from the past or a new analog version, you'll be converting again to digital, processing the signal, then coming back to analog -- more of these aforementioned conversions.
Finally, I'm not saying you shouldn't do what you desire, just saying that you need to think through what you're intent is and what you want to achieve, because if it's a true analog sound, you might want to stay in the analog domain and record to tape, or stay in the digital domain and use tape sound plug-ins and saturators.
If all you want is to mix with a physical analog "feel", that's what the Remote mode is for -- it can control your DAW faders, Pans, etc., so you can enjoy the tactile feeling of using physical controls rather than mixing with a mouse, track ball, or touch pad.
There are so many ways to go that it's very important to define what sound you're after, and thaty will inform your options. Similarly, it's hard for us to help without a lot more info along these lines, but I hope this helps.
