Ok. I had a look around for otg, and found lots of folks who are doing this with phones as old as s2. Definitely the note2. Stock, not rooted. This will make the note 3 like a small desktop for me. Very excited! I travel all the time and run my small business off my phone.
Stock Android doesn't usually do this, nor to my knowledge the overlay additions from Samsung. You generally have to be rooted for this to work with a few custom exceptions such as the Nexus Media Importer.
That's why I said Stock Android. All my devices have been Nexus or Google Experience devices where OTG host function only came with root or ROM.