A steady CEL means you have a problem, but it will not damage the engine to drive. What most people don't consider is that when that CEL is on, you have no way of knowing if a second or third, maybe more serious problem may have occurred. So you don't want to ignore it for months.
Anytime you get a CEL and take it to the shop, it is a good idea to get the actual codes. They will be in the format [P1234] That provides a lot more information than "It's the converter" there is no code that says it's the converter. That is someone's interpretation.