If you used alkaline batteries, yes. The electrolyte is potassium hydroxide, which reacts with CO2 to potassium carbonate (that are the white crystals on leaked alkaline cells).
General advise: No matter what chemicals you have there, you should remove them with a special cleaning fluid for electronics or rubbing alcohol/isopropyl alcohol. Remove the corrosion as good as possible. Let it dry completely before inserting new batteries.
If you have a multimeter, test the conductive paths on the corroded circuit board.