It may.
The most functional part of a catalytic converter is a ceramic substrate honeycomb coated with platinum-palladium, the actual catalyst. When molecules of bonded nitrogen and oxygen come in contact with the hot cataytic surfaces, the bond betwee the nitrogen and oxygen is weakened and the molecules seperate into nitrogen and oxygen. That provides the oxygen necessary for the “second burn”, wherein carbon monoxide molecules can pick up an oxygen atom and become carbon dioxide molecules. The nitrogen is considered harmless by itself.
If the catalytic surface coating is coated with residue of burning oil (carbon) than the NOx molecules cannot come in contact wil the catalyst and none of this stuff can happen.
However, since it passed emissions testing and you have no CEL light, you’re fine. Don’t fix it 'til it’s broke.