Not straight away as if it was a serious issue you'd get a message to shut down. We should remember that OBD codes were originally developed as a tool for monitoring emissions so it's not always something seriously wrong with the engine. Sometimes the engine light will go off on it's own after a certain number of engine starts but the code will still be stored for interrogation. I had that happen and the light went off before the code reader I had order was delivered and it never returned.
As said above, no need to panic. It’s probably one of the many sensors that’s just gone out of a predetermined range. Book the car in for repair under warranty when convenient.
There’s no need to spend big bucks on a code reader, the Launch CR319 does a perfectly good job of identifying fault codes and can also switch off the Engine Management Light (until it may or may not come on again later). That code reader is only around £20 and handy to have.
The engine management light came on in my 1200 mile C43 at the end of last week. As car was going in to have a scratched (on delivery) dashboard panel replaced, I asked them to check it. Car is still at dealer as they are working their way through 73 errors from the diagnostic. Hopefully it will be back to full working order today.