Courtney,
I think I've posted several times that the F-35B has a hard requirement (a KPP, even) to be able to carry out a ski jump.
So, the automatics will cope very well with a ski jump because they have been designed to do so. The aircraft won't be accepted unless it does. It just has to. I don't think I can be any clearer.
Initial design work started some years back, and even then it was clear that, as for the Harrier, a ski jump launch would be the lowest workload way to get into the air, with significant safety benefits and substantial improvements in payload. NoHoverstop's excellent answer provides great detail.
Hope this helps
Best Regards as ever
Engines