Yes
In a nutshell your relying on a third party to provide accurate timing data. That means the tracked satellites correctly reporting their position in the Nav data that your GPS receiver decodes.
The satellite is in an orbit and its position is regulary updated (every 12 hours) as it overflies one of 3 tracking stations (if I remember correctly, but this figure could have changed). If its updated incorrectly then it will cause your nav solution to be in error somewhere near to its own postion error. Also the satellite could go u/s and hence before its detected it could be providing incorrect data if it's not setting its health flag to unwell!
Not sure of the probabilities, but it has happened.
When I left this field of work autonomous systems were being developed to enable the GPS satellites to range from each other and correct errors in their modelled orbit to improve the accuracy of the system between the 12 hour updates of orbit data.
Also most GPS receivers are "all in view" systems. This means they can compute many position solutions based on different satellite constellations and throw away any satellite that seems to be giving an erroneous calculation. Not sure if the civillian receivers employ this technology (or even if the military ones have implemented it yet)
So there is robutness being continually build into the system. But as said earlier it only takes human or "mechanical" error and the system could fail. But that's the same with any system.