Yes, if the check engine light is on, it will not run to its peak performance. If it has say a bad O2 sensor it will run on a set spec which will allow it to run and not damage the convertor but it will not run very well. If there is a fault in the system, it can't run properly because something isn't telling the computer the info it needs.
Of course, difference codes will cause different problems in the way it runs but that is something different.
Craig