what if instead, people sell their bitcoin gold and use the funds to buy more bitcoin?
What we're going to see after the fork is exactly what you just mentioned. We've seen the same situation with Bitcoin Cash, people were trying to claim their free BCC just so they can sell it for more BTC. Bitcoin Gold has no future, so the right move would be to keep the majority of your coins in BTC, and the rest in other alt coins.
Bitcoin won't be affected by this fork, at least not by a large margin as many people predicted (price right now is 5491$). But don't expect a sudden surge in the price in the next few days. Give it a week or two.