No, it's not true, although I think this is a common misunderstanding.
Lime scale is the flaky white deposits formed from the calcium and other minerals found in "hard" water. Scale forms when you boil a pot dry, for example, and it is what eventually plugs up a coffee maker. "Soft" water doesn't have as much of these minerals, so less scale and soap scum form when you use soft water.
I think the confusion comes because table salt (NaCl) is used in home water softener systems. It is easy to get the idea that it's the salt itself that does the softening, but salt is just used to recharge (regenerate) the special resin in the softener tank. The resin looks like coarse sand, and water can easily flow through it. It's this resin that does the softening. Sodium harvested from the salt is stored in the resin. As water flows through the resin, the resin absorbs the hard water minerals from the water and releases sodium in the water to make the water "soft".