While my initial instinct would be to say absolutely not, there is the obvious fact that anyone obviously rich or famous would be likely to be slaughtered in general population of a medium or maximum security prison.
While this is true they could still put them in prisons that are more like the regular population
is sent to, but protected from bodily injury. They could still suffer the lack of privacy, intimidation,
and the not so fun chores most inmates are required to do.
After all it's the rich and famous that mostly decide how regular people are treated in prison. Perhaps if
they knew they would suffer the same treatment in jail they might consider reasonable changes.
As we know most of those who are rich and famous love being in control of their surroundings
and life style. Just loosing that would be quite a punishment.