Galileo is designed and will be operated as a Civilian system with additional features. Some of these features are that you can rely not only the accuracy of data but also on their integrity. The model is such that you can buy the guarantee that the system will work and delivers correct data. As there is no single military body involved, there won't be any degradation of the signal (esp. since such a functionality isn't built int in the first place).
The whole concept and orientation of the two systems (GPS and Galileo; Glonass doesn't really count) is completely different, the one a military system turned public, the other a public-private system useable by anyone with additional services depending on contract.
So, no, there wouldn't be any degradation would Galileo be operational.
And I don't even touch on the political aspects of all that...
If all else fails, immortality can always be assured by spectacular error. -- John Kenneth Galbraith