No.They would have to enter the SEPERATE process of citizenship.They would have to do it at the back of the line(meaning they would have to go home or get asylum)Current immigration laws would deal with that.Pence's plan is distinctly SEPERATE.Please reread the bill slowly.I think you will start to get it.
I suggest you reread it. Nowhere does it say that the W visa holder must go home to apply for citizenship. Please provide the language that says that.
I used to be in the business of issuing visas overseas. Asylum laws have nothing to do with this program.