No way. Lead battery chemistry is based on the presence of the concentrated sulfuric acid. Just like you can't bake a cake replacing flour with sand, you can't make an acid battery work replacing H2SO4 with KOH.
Not to mention the fact that adding concentrated KOH to concentrated acid is asking for troubles, as the mixture gets hot and starts to boil, splashing around. If confined in the box it can probably even explode.