No, there is no way this will happen. Not unless you significantly redefine what you mean by "passenger airplane" or "battery".

The energy densities of batteries (~1 MJ/kg) are simply orders of magnitude too low compared to liquid fuels (~50 MJ/kg). Perhaps they could get part of the way there by ejecting batteries out the back of the plane after they're used.

As green as I am, even I am quite pessimistic and skeptical of why airlines periodically try to experiment with biofuels - for publicity reasons or what not. Inevitably which get canceled after 12 months of halfhearted experiments. $23 per gallon doesn't make sense no matter how green you are.