One of the Galileo Open Service (OS) frequencies is quite close to the GPS Coarse/Acquisition (C/A) frequency. They are both around 1.5GHz. OS also has a second frequency, which like the two frequencies used for the GPS Precision (P(Y)) mode allows greater accuracy.
I would imagine that this means that with a suitable software upload (and assuming the modulation scheme is similar), a current GPS receiver could work with the Galileo OS mode, but not at the greatest accuracy it's capable of. You would need a receiver which also operated around 1.2GHz to achieve that.
Having said that, by combining fixes from both GPS and Galileo, you should be able to increase your accuracy to above that provided by each individual system in isolation.