Ebbie, If I was planning this for myself, I'd go for a week. I'd find out how much money the folks have in a week and live strictly on that, and I'd make myself learn to clean up and go to work using the facilities available to the true homeless people..and tote my 'homeless stuff' to work instead of stashing it somewhere that isn't available to others. A week is long enough to learn stuff that would be missed in an overnight outing. Surely there's more to it than sleeping.
With an overnight, I think it would be hard to keep from leaving some with the impression that you were like The Rich Man Who Ate Beans. The fuller stories won't come out with an overnight. You obviously already see your folks as People. If they're inviting you to join them, there's obviously an idea that you're Something Special..but if you're the person they count on for help, you're not necessarily a Person in all eyes. An overnight will probably break your heart. A longer stay would help put it back together and let you see more clearly.
In my last job, my supervisor pulled out a few loose papers to tell me about another project I needed to keep in mind. It was a half-assed program that was designed to 'help' migrant workers in our area. I didn't even know we HAD migrants so I asked several questions. She didn't know anything about it and I was disgusted. Before I was hired, she had been covering my position for a couple years. The program had been directly in her hands through that time and had been under her since it began. That job was with an organization that should keep their ducks adequately lined on their projects. That doesn't have anything to do with this thread, but it sets a clear comparison in my mind. Just by considering the idea of giving homelessness a whirl, you shine a lovely light.
When people are willing to put effort into trying to understand the lives of others, it makes the world a little bit prettier.
I admire your willingness to consider something like this and hope you bring back some wisdom (or random observations) to share with us!