really depends on the oil, mix ratio, as well as engine RPM.
most lower-end 2 cycle oil doesn't burn as clean and will clog up the converter, as well as produce more smoke (particularly if cold)
in my experience, Amsoil intercepter tends to burn cleaner and doesn't smoke up a lot when cold, for reference i use 40:1 when i premix it, and just pour it in the oil tank on the snowmobile, so like 32:1?
and at 14$ a qt it won't kill ya too bad.
if you keep the engine low and cold, it won't heat up the converter enough. but if it's in higher rpm it gets hot and burns it off good.