Will iCloud upload duplicates if it tries to upload a backed up library on a new computer?
Background Information
I am running OS X El Capitan on my MacBook Pro. On my current installation, I have the Photos.app using a Photos Library on an external HDD. The Photos Library is 136gb and is synced with iCloud Photo Library where I have 200b of storage.
I reinstalled OS X, formatting the SSD, and got all my apps reinstalled. I then wanted to permanently keep my Photos Library on my internal SSD instead of the external HDD. I copied my Photos Library over to the SSD, held down Option and selected my 136gb Photos Library as the Photos.app library. I went into preferences and set this as my system default library for photos.
The question
When I open my 136gb Photo Library preferences in Photos.app the iCloud Photo Library option is unchecked. When I checked it, it warned me that I do not have enough storage in iCloud to fit 136b of photos. I only had 84gb remaining. It wanted me to upgrade my storage plan to 1TB. It doesn't look like it's smart enough to realize that the photo library I've got, the 136gb of photos & videos, is the same 136gb of photos & videos that it's looking at online.
When I tell Photos.app to just continue using my 200gb storage plan, it complains saying it won't be able to fit all of these photos on iCloud. Is it going to re-upload every photo in my library? Is it smart enough to analyze the photo libraries (Local and iCloud) and determine these all already exist in iCloud and thus don't need to be uploaded? I'm assuming it would, and in the end i'll have my library connected to iCloud and both places containing 136gb of data. The way their dialogs explain it though don't leave me feeling confident about this. The current status shows it is uploading everything again which makes me concerned about potential duplicates.
My ISP limits me to 250gb a month of bandwith, so re-downloading the library consumes half of our data for the month. I really want to just resume using the library I already had downloaded prior to formatting and re-installing OS X.
Any guidance would be awesome.
MacBook Pro with Retina display, OS X El Capitan (10.11.2)