Unofficial Honda FIT Forums - If my battery disconnects, will car keep running?

I have a 2008 Fit and after losing my radio station settings for the second time in a week, I investigated and found the positive battery connector was no longer sitting securely to the post. It was still there but not tight and could easily pull it off. I attempted to tighten it down and after my first attempt, I could pop it right back off again without much effort. I then found that compared to the negative terminal, the connector was not pushed down all the way to the base of the post. It almost seems like the post is tapered (I was doing this in the dark with a headlamp) and if the connector sits towards the top, the clamp even tightened all the way down is still not enough to confidently secure it to the post.. Anyhow I attempted to push it down as much as I could with a screwdriver while tightening it down and because of all the housing crap, I still don't think I have it all the way to the bottom of the post and I'm not 100 percent positive, it won't pop off again. I'm going to investigate more in the morning as well as to try and find a small size 10mm wrench.

So anyhow, I was wondering, if I am cruising down the highway and the clamp pops off the post again, maybe this time completely coming off, will the car keep running or will it die on the spot? It's a scary feeling. I know the alternator can provide power once started but does it still need a connected battery to complete the loop?