A quick test of desalination via well:
I embarked on a seaside site, bringing along plenty of wood, some stone, some ropes, food, and no booze. I verified that activity zones on the oceanside and around the murky pools could not be designated as water sources, indicating that the water was salty, and therefore undrinkable without desalination.
I built half a dozen wells, three along the ocean and three in various murky pools. All of these wells showed as 'Active', meaning that they were usable as water sources.
Note: I did not set water source zones around the wells. Activity zones set as water sources are a completely different function than wells. It is not necessary to set a water source zone around a well, the dwarves will go and use any active and non-forbidden well as a water source. I did however try setting water source zones around the map to make sure the water was salty.
Very soon after the wells were built, thirsty dwarves began using them to get water:
The content of the buckets showed as 'Water laced with salt':
Despite the water being salty, the dwarves didn't seem to get any bad thoughts from drinking it.
In addition to the well over the murky pool, I also did the same test with buckets set directly over the ocean, with the same results.
I don't know if there are any specific bad thoughts or health effects from drinking salt water for years, other than the general slowdown and increased length and number of breaks from alcohol deprivation. I also have not tested if salt-water wells are usable as a source of water for prisoners or convalescing injured dwarves yet. If water from a well is always usable, there's no need to build pump-based desalination systems at all.
It does seem to still be the case that while wells don't desalinate water, dwarves are willing to drink water drawn from a well over a salty water source. You also can't judge whether a well will be usable by the ability to designate a water source zone around the well.