The reason why this will not work is the state has a interest in Planned Parenthood and the National Abortion Federation being around, where as the Catholic Church is non-secular and naturally open to scrutiny.
If we are successful at that, there are several reasons why it could toss these organizations into a financial tailspin from which they would never recover
It would be a beautiful thing, but it will never happen. There are way too many judges to see that the lawsuits are tossed out.
Hate to sound naive, but there's a National Abortion Federation? Who would work there? Could you imagine giving out your business card?