Not sure to be honest I don't know if the UEE has the file upload option that just was patched in. This is what I found on battlenet. Not exactly clear to be honest.
Short answer, yes!
Longer answer:
http://us.battle.net/d3/en/forum/topic/13660715952#6
In an upcoming console patch for PS3 and Xbox 360, we'll be enabling what we're calling "cross-brand" or "cross-generational" transfers for Ultimate Evil Edition. As the name suggests, these transfers will allow players to copy their character save data across brands and across platform generations.
We'll have more details to share once the patch is live, including how to complete a transfer with step-by-step instructions and how Battle.net account linking works. In the meantime, here's a quick list of what's supported:
PS3 > Xbox One
Xbox 360 > PS4
PS3 > PS4
Xbox 360 > Xbox One
The goal of cross-brand/cross-generational transfers is to support players who may have switched brands when next-gen systems were released for PlayStation and Xbox, but don't want to leave their progress from original Diablo III behind when upgrading to Ultimate Evil Edition.
As a follow up to that, please note that the following cross-platform transfers will not be supported:
Xbox 360 > PS3
PS3 > Xbox 360
For same-platform upgrades to Ultimate Evil Edition (PS3 > PS3 and Xbox 360 > Xbox 360), your character save data will be automatically loaded once the game is installed. No additional steps needed!