Clarification neeeded: Do you mean power the bicycle's motion with a battery? Yes, they have electric motorized bikes. Or do you mean power the lights with a battery, instead of the white wire? Yes, that can be done as well. I have a 12v 7ah lead-acid battery powering a nice bright light on my MB.
Third option- do you mean getting the power for spark from the battery? Answer is- theoretically yes, but hard and you would still have to time it somehow...and again- why?
And if you have an electric start you might cross into the area of your bike no longer fitting a certain classification and instead being legally classified as a motorcycle... which requires licensing, special driver's license endorsement, insurance, tags, tax, title etc...
