If the emissions system is working correctly, I would leave it. The air pump is there for a reason: to burn off unmetered fuel in the catalytic converter. Without fresh air coming in, your catalytic converter will plug with carbon and die prematurely.
Yet some models never came with an air pump. Curious. No, I don't think the thermactor is an issue to remove, but beware that you may get a gunked up cat, or it may leak if you don't crimp off the tubes.