Oh hell yes. GPS is the basis of trillions of dollars of business globally. Just look at sea shipping and aviation alone. Would a lack of GPS ground every commercial plane? Maybe.. maybe not... but it certainly would be a huge disruption.
The first time it happens everyone would just drive hard to making sure all "GPS" systems were actually multi-system GNSS systems. Which is already true of most consumer phones, but I imagine there are still plenty of GPS-Only stuff out there. After the first GPS shutdown and the time for retrofit, everyone would have support for Galileo etc... and the Europeans would be standing there going "SEE!!!! I told you we can't trust the Americans!". And they'd be right.