My two cents:
Most professors are either knee-deep in research, teaching, or don't want to be bothered with anything during the summer, so rarely will sending anything this soon be helpful. Secondly, while e-mail is great at quickly getting in touch with people, I hardly consider it memorable. I had professors for my undergrad that wouldn't even read mail sent from outside the university, if it even made it past the spam filter. Write a letter and mail them if you're gun-ho about writing a POI, just include your email address for easy communication on their part.
Personally I don't believe a POI letter will do much in the way of getting accepted, unless it's a smaller less competitive program, but there are exceptions to every rule.