That's exactly how it works in every service yes. It's impossible to have +300$ as fees logically. Just as a tip, It's early a little bit but make sure to move your coins out of Coinbase before 1st August.
Thanks everyone for the help.
But now to address the quote. I'll get my coins out of coinbase, but the article below seems to think that even moving them to a wallet may not be enough. Is a standard desktop wallet good enough to shield me from what will happen on august 1st? Or do I need a hardware wallet?
From the article:
"If you don’t control your keys during a chain split three main things may happen:
1. Your bitcoin balance will stay the same and you will be able to use that bitcoin token as usual.
2. Your bitcoin balance will be
zero over night since your wallet chose the wrong chain
3. Your wallet provider will offer you a chance to keep your token balance on both chains or to choose one of them"
https://hackernoon.com/casual-bitcoin-users-you-need-to-know-about-aug-1st-d568e07418cb