My response:
If your insurance policy lapsed at 12:01 a.m. on the day of the accident, which occurred later that evening, then the answer is "No." This is one of the reasons why, when reporting a claim, an insurance adjuster will ask not only for the "date" of the accident, but also the "time". Once the time of the accident is known, and that time is after a policy has lapsed, you will be denied coverage; and, you're on your own.
IAAL