Not necessarily. Years ago I used to be a store manager for Leslie's Pools and a large number of customers had salt pools. In most cases after a good 3-4" of rain most people would only have to add a bag of salt to a 18K gallon pool (average size B.Y. pool) to bring it back up into range. Now this of course is at a concentration far below sea water, but dilution would not necessarily be as severe as one might expect. My parent's pool only needed two bags after Harvey and they got 9.5" of rain. PH and ALK stability would be of greater concern from rain. When it rains, the water tends to be acidic so it will pull the PH and ALK down. In a salt pool this is not an issue as these typically run high because of the creation of sodium hydroxide (PH of 11) as part of the system creating chlorine via electrolysis. But in a Reef Pool you would need to add a reef safe buffering agent to prevent the rain from pulling the PH and Alk down.
To really pull this sort of thing off in our area, you would really want to have a transparent awning like glass over the pool to block the rain that can be closed off for temperature and humidity control for the 10 months of the year it's 90 degrees outside.
Yes, I owned a saltwater pool for 10 years. Correct, PH and ALK were important element to keep track of. A lower PH is always needed to allow a salt chlorinator to produce the chlorine. Rain actually made the PH go higher and I would have to control it by adding my acid and testing the buffer. While saltwater pool and reef pool isn't the same, design is key, I had a lot of run-off from my roof and all the leaching from rock, as a result, I had to add four bags, stabilize, and a larger dose of acid over a longer period to bring my pool up to par. Again design is key. I also had levels of water falls, so that collection from that area added to the dilution. In the years I had to pool, a concept of building an outdoor reef was something that I looked into, unfortunately, doable and fun, but funding would be an issue for me. Wanted it to be a hobby, not a job.