Yes, a discharge battery can affect both spark and fuel mix. Actually had a similar issue when I replaced all my injectors. I had the radio and lights on the whole time. Battery would turn it over when I was done, but it wouldn't even fire. I finally gave up because it was 2am and I had to be at work in 3 hours and it's an 80 mile drive to work, so I called AAA and had the van towed near work.
They put it on a charger, and it fired right up. If the voltage is too low, it makes the injectors squirt instead of spray, and combined with weak spark, the plugs get wet and won't fire.
