Quite a bit, actually - according to a New York Fed Staff Report by Joshua V. Rosenberg and Leah G. Traub. Their report, Price Discovery in the Foreign Currency Futures and Spot Market, compared price discovery in the foreign exchange futures and spot markets "during a period in which the spot market was less transparent but had higher volume than the futures market".
We develop a foreign exchange futures order flow measure that is a proxy for the order flow observed by Chicago Mercantile Exchange pit traders. We find that both foreign currency futures and spot order flow contain unique information relevant to exchange rate determination.
When we measure contributions to price discovery using the methods of Hasbrouck and of Gonzalo and Granger, we obtain results consistent with our order flow findings. Taken together, our evidence suggests that the amount of information contained in currency futures prices is much greater than one would expect based on relative market size.