The EGR Valve strategy as it is designed for the 6.0 is a sorry piece of work. Between real issues and mis diagnosed issues the EGR Valve has been the disdain of owners, dealers, and Ford.
It seems that when the EGR Valve goes there tends to be a cascade effect thereby, creating even more problems.
I doubt that there would be a Cat converter issue. But, if there was a premature failure with the converter I would rather sacrifice that than all the other components that are affected by the EGR Valve.
Mine has been diabled for almost 15,000 miles. I have no negative issues with my truck.