Never tried it. I frequently settle on islands, but have other ways of dealing with the issue.
I tend to most often choose a not overly small sea island with at least one adjacent tile of water non-freezing (not all sea water freezes) and a path through non-freezing sea tiles and land tiles that allows me to reach mainland (and/or several islander villages...mainland preferred, though) in some way and preferably also allows for some paths towards one or two other medium-sized nearby islands.
Generally such paths aren't very efficient compared to the usual rowing or icewalking* routes--sometimes even very inefficient--not seldomly am I required to travel 4x the number of tiles the most efficient icewalk or row routes take, plus the constant zoom in to reach shore, pick up punt, walk to the point I can zoom out, do so, drop punt, hit the water again, rinse and repeat every time my route requires me to hop over a minor island--but suffice well enough that I *can* reach civilization when necessary and I tend to mostly plan matters so that I do not require many trips back-and-forth during weak ice, either by having various on-home-island time and labour-intensive tasks to work on during those periods or by spending most of that time either on nearby islands or mainland.
*that is, if there is a direct icewalk-to-mainland route available, which isn't too common. Most of the winter months, even those with strong ice, require a mixture of overland (or overice) and water travel. The further off-shore, the more likely that becomes. Unless one happens to live in one of the Island territories smackdab next to an island with one or more islander villages on it. One of my current characters is lucky enough to have both an over-ice and fully-overseas route from island to mainland (so no island-hopping needed) available during winter, but that's pretty rare. Neither of those routes are anywhere near a straight line to mainland, though, and both land me on mainland about half a day travel from the nearest settlement even though the summer oversea route to nearest settlement is barely half a day in *total*.
Occasionally I settle on very large sea islands, though as I strongly prefer to settle on islands without NPC villages, those are somewhat rare. In those cases, I can--after acquiring all the necessities for self-sufficiency--easily go months in-game without requiring contact with civilization: plenty of large animals, foreign traders and njerps are generated on those to keep me from lacking things to do. The same goes for picking those islands as with the medium-sized ones: ensuring an existing, even if non-efficient, route to civilization.
For freshwater islands, strategical placement of rapids works but it can be somewhat difficult to find an appropriately-sized island that connects through rapids to either the lakeshore or through a chain of other islands eventually leading to lakeshore. Usually easiest when at least one side of the island is bordered by a river rather than a lake, but even in some large lakes you may find fitting islands. Just takes a lot more looking around.