It's a spectrum of risk. A copper heat exchanger is more susceptible to corrosion than a cupro-nickel alloy or a titanium heat exchanger, but it doesn't mean that it will definitely corrode too quickly at SWG salt levels (typically 3000 ppm). There is no question that it will corrode faster, but as to whether this will be a problem before the heater would fail for other reasons, that is not certain.

Given how many people have converted to SWG pools, I think the copper heat exchangers aren't the biggest problem -- at least that isn't the most common complaint. The other items waterbear mentioned seem to be the more common issues -- namely, cheap stainless steel or regular steel (or even zinc) used in screws and some softer stones used in parts of the country that also don't have regular summer rains. "Vanishing" aluminum headers on automatic covers and aluminum tracks are also a problem, but are usually mitigated by using a sacrificial anode. In fact, you could at least partially protect all the metal in your pool by attaching a sacrificial anode (usually zinc; sometimes magnesium) buried in moist soil to the bonding wire.