Yes, I place the jack here on my convertible. I've never had an issue. My convertible does have a little cowl shake. Sometimes the toneau cover rattles a little in rough parts of the road. My mom has an 03 Thunderbird, and funny enough that car rattles a lot when the hard top is attached, more than my Reatta any day.
Below are a few photos of my car that I took in 2014 at Cumberland Falls State Park in Kentucky.
There is a beautiful lodge in the park, DuPont Lodge, that everyone should see if the are in that area. Here are some of photos of the lodge and the falls.