I don't think (American) GPS currently supports that for the civilian signals, though IIRC Galileo does and there are plans for the American version to support it in the future.
However, GPS signals are essentially just the location of the satellite with a time stamp. There's nothing to prevent the signed signal from being re-broadcast a short time later to mess with location data. The Russians have (allegedly) been doing this in the Black, Baltic, and Berants seas the past few years.
Don't believe it's yet publicly available for Galileo, but yes, it's meant to be going live soon. (And note that the authenticated stream is a paid for service.)
However, GPS signals are essentially just the location of the satellite with a time stamp. There's nothing to prevent the signed signal from being re-broadcast a short time later to mess with location data. The Russians have (allegedly) been doing this in the Black, Baltic, and Berants seas the past few years.