I typically do large water changes on my tanks and have not had any adverse effects, on either coral or fish. My corals will typically close up during a water change no matter how small or large though.
With the amount of nitrates you have I would not be too overly concerned. However, if you do have corals or algae now would be the time to remedy the situation before it escalates. How often do you generally do water changes and in what amount? You can up the weekly or bi weekly changes by a little bit each time until you get the levels down or you can do several large changes to quickly go after the issue.
With my tanks I tend to do a 50% water change every two weeks on my larger tanks, 90g and 125g and more frequent but just as large changes on my 60g and my 29g. I also am a very bad overfeeder so I know the origins of my issues, once you address where the excessive nitrates are coming from you can move forward by adjusting your behavior or just doing super big water changes.
I have to add though, my tanks are all pretty well established and have been up at least 2-3 years so the tanks have matured to that point where water changes are all thats needed pretty much. I do very well with the large water changes but each tank is different and results may vary. As long as the water is matched in temperature and salinity you really shouldnt have any problems. I would caution that if you have any new additions that you should stay away from a super big change until they are acclimated and happy in the tank so you dont cause more stress on an already stressed piece of livestock. Water changes can be traumatic on livestock at any point but more so when they are still new to the tank.
Hope that all came out right, its getting late and its been a long night for me. lol
Good luck!