That will depend on the acid.
Leaves are protected by several barriers, such as a wax coating, and thick cell walls made of lignin, cellulose, and pectin, none of which react very much with most acids. But they do eventually react, if slowly. That is why special acid-free paper is used for artwork and archival documents. Paper is mostly cellulose, and acid will eventually make it brittle and yellow.
Strong acids like sulfuric and nitric acid will dissolve the leaf. The thinnest parts of the leaf will dissolve first, since there is less material there. The result is a lacy, delicate web of the ribs of the leaf that give it strength and structure. You can then neutralize the acid to prevent further corrosive action, and preserve the lacy leaf.
Living leaves have pores in them (called stomata) that allow them to breathe. If acids get in these pores, it can kill the cells inside the leaf.
Dead leaves have less protective wax on them, and they can absorb water and acids more easily. The dried leaves are thus more prone to attack by the acid, and will deteriorate faster than a freshly picked green leaf.