Artistically, yes, it's definitely possible. Technically, no, or at least most of the time.
Most DSLRs will be able to give better resolution and render details better. And in most circumstances DSLRs will outperform compacts in terms of degree of noise at high ISO levels. Along with that, you also get improved responsiveness with a DSLR.
The downside is of course the size and the cost. Because these systems are so large they may attract unwanted attention as well.
In the end, the user's skill level is the greatest contributing factor to the quality of images produced. Certainly there are some things that a digital compact cannot do, or cannot do as well as a DSLR would. This is why some still don't mind forking out extra cash for an SLR system. But if you give a skilled user a compact and a newbie a DSLR system coupled to a lens yielding the same focal length range, the photos out of a skilled user will be more intriguing and attractive, artistically, and perhaps in some cases, technically.
If you get a chance to do more with less, or work with minimal equipment, give it a shot and it may be an eye-opener to you. I am about to do that myself...embark on a holiday with just a compact film camera, one kind of film and a fixed focal length lens. Even if the results turn out disastrous, at least I know I have tried.