Theoretically, it probably is possible. It's been done on the AT&T version, which suffers from the same problem of the locked bootloader. You would have to be rooted, and use Mobile Odin, which does not install the bootloader. It should be possible to run a hybrid firmware with 4.1.2 OS and the 4.3 bootloader and modem (don't try to downgrade the modem) via this method. However, it's probably more risk than is necessary. IF you attempt to be brave and use this method, make sure to back up your EFS, because if you lose that, then something like the phone not booting will be the least of your worries. Would be advisable to have the 4.3 official firmware and Odin ready, in case it doesn't work out.
I do not recommend this method, especially for those new to the Android and / or flashing world. Any attempt to do something like this is solely your risk and responsibility. I only provide the info of possibilities. I do not have a VZW S3 in front of me to try, nor would I probably bother if I did as the benefits do not outweigh the time and potential for trouble.
Need some help, advice, something fixed? Hit me up on Hangouts @ es0tericcha0s and check out my site: http://mobilemojo5280.com
for more info!
HTC Droid Eris / Motorola Droid / Samsung Galaxy S Fascinate / Motorola Droid X / LG G2x / HTC Evo 3D (x2) / Samsung Epic 4G Touch (Sprint S2) / HTC Amaze / Samsung Galaxy S3 (International) / Samsung Galaxy Note 2 / Nexus 4 / HTC One / Samsung Galaxy S4 / Sony Xperia ZL / Nexus 5 / ? (One+1 maybe...)