So if I hold Bitcoin on coinbase (and I do). What will happen with the fork? I get nothing?
I think that it's just Yobit that has made an official statement on supporting the fork and others are still unclear about the same.
As ShadowBJ21 said, there might be something shady behind the scenes and the drama has since been heated up with the use of "name" only and that, the so-called "Satoshi's coins distribution to those who will support the project" statement looks very slanderous on their part. Try not to fall for their tricks if they ever ask you for your private key input in order to get those "free coins", you might end up losing what you already have.
Sometimes, I wonder the calibre of people that are running that Yobit exchange that everything is what they support without even taking their time to study it to know if its acceptable by the community the moment there publicity is there, they start with future trading and thereafter start crediting their customers who have bitcoin in their wallets. Its just totally loss of direction.
So if I hold Bitcoin on coinbase (and I do). What will happen with the fork? I get nothing?
The former SegWit was what I read coinbase to be supporting but for this one, there is no statement yet and only if they are compelled to support before they will have to credit users just like the case of BCH. I suggest you move your coins to an offline wallet to be on a safe lane in case they choose not to support eventually.