Yes, an acid start-up removes most of the calcium hydroxide on the plaster surface. Therefore, the plaster finish is no longer smooth and dense (as seen under magnification) as it was when newly finished and before filling the pool with water. That means the surface has been aged somewhat and will stain easier over time and not last as long as it would have with a better and non-aggressive water start-up procedure.
An acid start-up is so acidic and aggressive, that it prevents the dissolved calcium hydroxide in the water from becoming "plaster dust" by keeping it dissolved. The dissolved calcium hydroxide is converted into soluble calcium bicarbonate via the aggressive acid start-up.
Plaster dust is formed by the calcium hydroxide reacting with the alkalinity (bicarbonate) of the pool water to form insoluble calcium carbonate (which is what plaster dust is). An acid start-up removes the alkalinity in the water so that calcium hydroxide does not turn into plaster dust.