Cats are already shot from mentioned oil consumption levels. And it would take a whole lot of two stroke oil to cause any catalytic converter issues. Like 5:1 ratio, but at that ratio engine simply won't run. An ounce of TCW3 oil per 5 gallons of gas isn't enough to kill a cat, too diluted. Age seems to kill catalytic converters way before any chemicals get a chance to do so. I've seen lots of catalytic converters that just crumbled over time, and little ceramic particles made it's way back into combustion chamber, killing the piston walls and cracking rings in the process.I didn't get the impression that OP was talking about adding the 2 cycle oil to the sump, I assumed he was talking about adding it to the fuel, but I could be wrong.
I agree wholeheartedly - never put 2 cycle oil in the sump. A far as adding it to the fuel, the only thing that gives me pause is what that might do to the catalytic converter and/or O2 sensor. I don't know it's a problem, but I don't know it's not.
If you mixed it as dilute as someone above mentioned (640:1) I have trouble believing it would cause an issue.