In short, to answer the "are the leftover chemicals that were the result of neutralized acidity (or alkalinity) actually bad for the fish?", I think the answer is no. You're either adding (bi)carbonates to buffer the acidity, or using something that, if I'm not mistaken, will bind the (bi)carbonates to lower pH. RODI is, I believe, the EASIER way to go about this. Start with zeros across the board and simply add what you want.
If you're asking about putting fish in pure, un-remineralized RODI water...they will die. No osmotic regulation, potential for wild pH swings, zero water stability.
In regards to the hypothetical question, I have no idea. Yes, you can absolutely neutralize the acid by simply adding baking soda or another carbonate source. There will be a reaction, however, and I'm not sure what the leftovers will consist of. Call me crazy, but I don't think I'd put fish in it! lol