How long does gap insurance take to process?

My friend just TOTALLED her car and her insurance only covers rental for three days once they declare her car totalled. She doesn't have to worry about it because her car is paid off but now of course that planted the seed in my head of what happens if I have an accident I got Gap cause I rolled in about 6k negative and now with the miles I have on it I am probably about 10k upside down so is it going to take forever, am I going to be covered until they get my gap payment will I be able to get another car if it takes them a while to recieve it. Will Gap cover that much so many questions. And the reason I am asking is my friend is a safer driver than i am and she was hit by a drunk driver in the middle of the afternoon, so now of course I am petrified that something is going to happen (I AM A WORRY WORT I KNOW) chances are they wont happen but they still might so I just want to know