I agree with Sharon, David. Try it with one plant first. IF you are going away for a few days, setting the plants in a pan of water will probably help them not to wilt until you get home, but I'm not sure your Zinnias will like it.
Coleus and Zinnia are very different plants. If you look at the stems of Coleus you will see that they are full of water, and the plants can take any amount of water, it seems. They thrive here when we get heavy downpours of rain every day in the summer. I also have one growing in a 6in. deep pan that holds a lot of water, and it is very happy. I've kept cuttings growing in water for months, too.
Zinnias like conditions much drier to bloom well. Look at their stems - quite solid and drier or more woody than Coleus. When I have grown Zinnia, even in Utah which has a hot dry climate in summer, I didn't need to water them every day. They liked to dry out between waterings. Here, Zinnias grow and bloom well in the springtime (our driest season) with hot, dry, sunny conditions but as soon as the rainy summer weather hits, they die off. So my bet is that if you grow a Zinnia plant in a closed watery system, it will rot or drown. But
I really don't know for sure because I never tried it.