Yes, I think so. after the yeast is done and settles into dormancy, the temperature inside the fermenter will equalize with the ambient temperature whether that is the air temperature of the room or the temperature of the swamp cooler. I find that once primary fermentation is done, I don’t have to add any more ice. Of course, it depends on the ambient temperature of the room/area.
I’m not aware of any rules of thumb regarding how many degrees over the wort/beer temperature will do the trick. I would just say to add ice until your fermenting wort is at optimal temperature and then remove or add ice to keep it where you want it.
I did this for years. I would pitch a couple degrees below target, and swap frozen water bottles at least twice a day. I found the temp of the water in my tub was pretty reliably within a degree or so of the fermometer reading. As you’ve noticed, the trick is to change those frozen bottles for the first 3 days or so to try to keep the water at your target temp. After 3 or 4 days (average strength ales), I took the fermenter out of the water and allowed to warm up to room temp until I reached FG, to help the yeast attenuate and clean up. It takes a commitment those first few days, but I got good results.
Yeah, when I started I didn’t know whether to have confidence in the fermometer strips or not, Denny. But after a while it was obvious that the readings were pretty much in step with each other.