I don't think it would technically be prostitution. Lots of mistresses are supported by their married lovers. They aren't getting arrested left and right.
If he is paid by the hour or by the activity, that might raise legal flags. But offering to support someone in exchange for companionship...happens all the time.
In the scenario laid out by questioner, the woman is having a lawyer draw up the paperwork; from which we can infer that the lawyer doesn't think this arrangement is illegal.
Would I do it? I don't know. That's one of the situations I'd have to be in to know what I would do.
I can't honestly say that I think it is a bad thing for someone else to do, either.
Let's assume, for the sake of argument, that this situation is NOT illegal.
What we have is a person making a living off his personality and to a certain extent - his body. Which many celebrities and professional athletes, and models, do.
On other issues, I support a person's right to do as they choose with their own body (being pro-choice, DNR orders, living wills). My reasoning on those issues is that indeed; our bodies are ours to control - even if we choose to "sell" them to somebody else.
Before someone asks - yes, I would favor the decriminalization of prostitution.