To answer your question the answer is yes and no. Excess ascorbic acid breaks down in to oxalic acid. Oxalic acid is problematic as it can lead to kidney stone formation, is a tissue irritant and it binds iron and calcium. So excess ascorbic acid will lead to excess acidity in this manner.
The acidity of the ascorbic acid though is really a non-issue though as the body regulates its pH readily except in very rare occasions. Normal levels of ascorbic acid leaving the stomach will be neutralized by bicarbonate just as stomach acid and citric acid from lemon juice are.
Ideally though vitamin C should be derived from food or herbal sources. The vitamin C in these sources are generally stronger and more stable than synthetic vitamin C (ascorbic acid), which is highly unstable. Natural sources also contain the synergistic bioflavonoids needed for the vitamin C to function properly. And if you are worried about the acidity of the vitamin C still the vitamin C from plants is naturally buffered by the minerals in the plants.