I think tanks can do just fine without a skimmer. Especially mature systems that have been maintained properly.

The thing that is going to make it give very different results for different tanks is that it depends so much on an persons stocking & maintenance & feeding habits. Even more variable will be each systems ability to export/utilize excess nutrients. This will vary depending on things like how functional the sandbed is (mainly infauna variation), type/porosity/ amount of liverock, types of corals, how established the bacterial populations are and types of established bacteria, probably many other things too.

Going skimmerless isn't something I would recommend to the general public because of those different factors but I think many people can get the same or even better results without a skimmer. I think the safe way to do it would be to wean your system off of the skimmer so that it gives your system time to adjust to the higher availability of nutrients.