That's not how it works. As APD said, the new document will replace the old document within ERAS. If I've already printed out an application and subsequently download a new PS, I have to print out the new PS and physically replace it in the review packet. To be honest, that may or may not happen--this time of year it's a struggle to keep up with applications, reviews, invitations, responses, and schedules. Replacing personal statements in already-prepared review packets just may not make it onto the high priority list. However, if you replace your PS before I print your application, the new version is the only version that's available. Unfortunately, there's no way for the applicant to know whether a program had already printed the original document.
If you are offered an interview, you could politely ask the coordinator to make sure the newer statement is the one in your application file when you contact him/her to schedule your visit.