Yes. You would have to use the analog outputs of the Dish box to the analog inputs of your DVD recorder. And, no, Dish does no make it impossible nor in any other way hinder such recording devices (that is not imposed by the content owners or providers), in fact, they support it, especially the Archos external recording device. You can use the VCR Timers that every DishPro box has, including the DVR boxes, to coordinate the start and stop times of your recording device and the box tuning to that channel. The Blaster feature of the Dish boxes (which automatically tunes to box to the correct channel and start the RECORD function of the external device) was designed for VCR's, so your DVD recorder may not have a supported code because DVD recorders were and are still nowhere near as ubiquitous as VCR's. You may have to manually program a timer in your DVD recorder to match the Dish box VCR timer so that the DVD recorders begins as scheduled, and at the same time, the Dish box will turn on and tune to the correct channel and then turn off at the end of the show. You can set the VCR timer using the Dish EPG--up to 48 hours in advance on NON-DVR boxes and 9 days on DVR boxes--for added ease. Otherwise, you can set up a MANUAL VCR timer and specify all relevant info yourself using the prompts.
However, if you get an HD DVR, or box, your recordings to your DVD recorder will only be in SD. A diminished experience upon playback on your DVD recorder. Why don't you just go ahead and get the Dish DVR? It is so much better and with more, easier features and will playback in HD, and you can use your DVD recorder for recording stuff (and playbacks) of shows you want to keep. That's what I do. There is no comparison to the the power of the DVR to allow me to get the full value of the channels for which I pay and for its far superior ease of use--and TWO tuners with Picture in Picture--that my DVD recorders just can't match. I use my DVD recorders a lot, for personal archiving, but not as my main DVR machine. Heavens no! You will find the DVR and huge leap forward.