You can certainly run a tank to some degree without doing water changes, lots of hobbyists have done it in different sized systems. The problem is the limitation that puts on your system. When you do water changes you're doing more than just removing nutrients. You're adding a lot of trace elements, trace being the key term here. Meaning they're immeasurable by today's standards unless you work in the right lab. Does that mean you can't grow certain corals, or have certain inverts? Probably not, it just won't be an ideal scenario, since you can't dose what you can't affordably measure.