Not an issue, they will see it anyway. Lots of people choose incorrectly.
If you submit a second PS, it replaces the first. If a program has already saved your app as a PDF or printed it on paper, they will have the old one. Else, they will just see the new one.
Regarding personalizing PS's -- IMHO it's only helpful if you really have a connection to a program or area. Every year a few people just decide to add our program's name to their PS, and it's clear they will just put another program's name into the same spot for each place they apply. This is fooling no one, and not helping you at all. Saying generic things like "you have great research opportnities" or "I saw your fellowship match and it was great" are really meaningless. And if you send the wrong PS to the program, that's a disaster.