I imagine a 1TB drive would work, but the physical size of the drive is still limited to a 2.5" form factor and less than 14mm in height. The 500GB drive I used was a 12.5mm and it had no problem fitting inside the case. Most newer 1TB drives are 9.5mm, which wouldn't be a problem. The only problem I could see is if the Korg IDE controller doesn't understand the newer AF (Advanced Format) 4K sector layouts; but most newer drives will do 'on the fly' translations seamlessly in the background - without the IDE controller knowing. I choose an older 500GB drive that used the standard sector formatting, so the issue never came up.
The main thing to remember is that the Korg uses an older IDE controller, so there may be some limitations and compatibility issues to consider if you try to use a drive that big. In theory it should work - but I haven't tried it myself.