Q: Would this result in the check engine light turning on?

The check engine light indicates that the engine controller (ECU) has detected a fault in the system that could effect the exhaust emissions. The ECU stores a trouble code to help technicians diagnose the problem and lights the Check Engine Light to let you know. Sometimes you won’t notice any problem at all with the way the car is driving. Others it will be very apparent. I can’t imagine what fault would make your steering feel loose. I suspect that it is something else that has been creeping up on you and when you see the warning light on the dashboard, it makes you kind of hypersensitive to the car; making you notice things you haven’t before. You need to have the system scanned to see what the trouble code. If you contact Your Mechanic, they can send a technician to your home or office to scan your controllers and let you know what needs to be done. It would be a good idea to have them look at that front end too.