JSONP is a way to consume a feed from a willing website on a different domain name. I say "willing" because the feed must be presented in JSONP -- there is no way for you to alter a JSON feed into a JSONP feed without using some sort of proxy.
Because you'd need to use a proxy on your domain to convert the feed to JSONP, you would then lose access to the client's cookies for the target domain. That basically means that no, you can't use a JSONP request to defeat the same-origin policy.
Because you'd need to use a proxy on your domain to convert the feed to JSONP, you would then lose access to the client's cookies for the target domain. That basically means that no, you can't use a JSONP request to defeat the same-origin policy.