Not much as their revenues are made of commission (in the form of buy/sell spread on the actual market price) on the transactions made on their exchange.
In this respect, Coinbase is basically like a traditional Bank operating in the FX market: regardless of a certain market movement in price, the Bank will always buy at a little below the market price and sell at a little above market price, thus always making a profit.
For this reason, Coinbase value is more tied to the average number of daily transactions effected on its exchange rather than to the value of Bitcoin.