This doesn't answer you question about MK, but i know that you can in the Journey into Your Imagination pavillion (home of FIGMENT ride ) in Epcot you can.
I am not exactly where it is in MK but it is with at leeast one of the banks of public phones. I can't remember which one I saw. FYI - a CM told me all resorts and parks now have these "e-mail/phones". I did use it at OKW and BWV but found it costly ($1.00 per minute) and hard to manipulate.
Oh, I just remembered I saw it outside the bathrooms by Aladdin's Magic Carpet.
I believe as you enter MK, you go immediately to the right before Mainstreet and there's a couple kiosks in the Kodak shop, similar to the one's in Innoventions. I hope someone else can verify that, but my wife says she saw one last. year...
There were some in the area that used to be the waiting area for the Walt Disney Story. The last time I walked through it, in January, they were gone. The ones in Innoventions are sponsored by IBM - so I wonder if Kodak dropped the kiosks?
I am assuming you're talking about the free e-postcard/photo kiosks and not the internet phones?