You can, the question is - should you?
This decision is highly dependent on your system. If you have a scrubber that keeps the nutrients where you want them, then obviously you don't need to do water changes for purposes of nutrient reduction. However there are other reasons to perform water changes, depending on your livestock. Some may stay healthier with regular water changes. Others may be just fine with none.
I attended a presentation by Bob Fenner a few years back where he discussed this issue. One thing that happens when you stop water changes is that all of your tank livestock (both fish and corals, but his topic in particular concerned corals) was that everything will get used to the "soup that it is in". Now, if you try to introduce anything new, it's likelihood of survival diminishes. This has to do with chemical warfare, essentially. Everything gets used to each other and there is balance. Changing the water occasionally upsets this balance a bit (for lack of a better way to put it).
His presentation also was about acclimating corals to a new tank by keeping them in a QT and then transferring water between the 2 tanks to allow the corals in each system "get used to" each other so when the new corals were placed in the tank, the chemical warfare would not be an issue (or as much of an issue). So by using that method, theoretically you could do no water changes and still be able to introduce new corals to the "soup"
For the record, I have 2 tanks I maintain (mine and one in an office in town) and I can't recall the last time I even mixed salt. If I had the time, I'd do some regular water changes. I just stay too dang busy....it's not LARS ;Drowning