First off, IANAC (I Am Not A Chemist), but...
The small amount of sodium bicarbonate will be completely consumed and will leave you with less sulfuric acid, plus the products of the reaction: Sodium Ions, Sulfates (S04), Water, Carbon dioxide. I think that carbonic acid is produced but decomposed into more water and carbon dioxide. The carbon dioxide of course bubbles off, so you are left with some sodium ions not normally present, replacing some of the hydrogen (H2+) ions. Technically you added water and water is produced in the reaction, but I don't think you have really diluted the acid; you have the same amount of Sulfates as before. You now have a mix of two acids: H2S04 and a little Na2S04. I have no idea what the implication of that is.
Curiously, I have seen discussion of using pure sodium sulfate as an electrolyte in lead batteries. So maybe the contamination isn't too deadly to the battery.