I am not even sure travelling with the NS would count for the P+R ticket (edit: your link says it does, but not for the full amount), even if you did it with your own (permanent) OV chipkaart.
Fortunately, there's a good alternative which certainly works: purchase a P+R GVB return ticket and take Metro 51 to Central Station (or any other destination in the city center). Much more flexible than the train!