I notice that TOR is going to be on sale super-cheap tomorrow on Amazon, so I'm thinking of finally buying it. However, the sale appears to be only for physical versions. My question is: when I receive the physical copy, will I be able to enter the product key on Origin and then be able to download it digitally, as one is able to do for some games on Steam?
You would have to download it from your disc, but once the client is downloaded and your product key is entered you will not need the disc anymore.
From memory, if you log in to the SWTOR.com website and enter your product key you are able to download the installer from Bioware's website. That only helps if the reason you ask is due to lack of an optical drive. If you want Origin integration then I don't have a clue as I don't use it myself.