Katherine is correct, I had an event with my fuel injected turbo charged Kawasaki on a trip that I thought was going to strand me in rural Colorado. Riding in the rain most of the day with a chip in my glass headlight shorted out the headlight circuit and was a huge draw on the battery. Hence as voltage dropped my fuel pump could not keep up and I limped into a gas station to try and figure out what was wrong. My first thought was a bad fuel pump because it was taking a much longer time to get to pressure up, that and not enough juice to turn over. Great, where am I going to find a 26 year old fuel pump in rural Colorado... My riding buddy said he saw my headlight dimming and acting weird so I pulled the headlamp fuse, turned her on and waited for the pressure to come up and bump started her in second gear and she fired right up. Quik voltage check while running showing 13-14 volts, and running fine. Got me through the rest of my trip, around 200 miles (daylight of course) and ran fine.
Long story short I believe if you have enough juice to get the fuel to pressure (not alot really) bump starting will get you on the road again.
