In Enter the Matrix, Sparks talks about "tons of agents" when he sees all the Smiths chasing Niobe/Ghost. He does recognize that he's Smith, though.
In Reloaded, Link refers to them as unknown code structures (paraphrased), not agents.
And Bane's operator on the Caduceus uploaded Bane's RSI together with Smith without even noticing it -- neither meanwhile nor afterwards. Obviously, he still saw Bane on his screen after Smith had taken over him.
Was Smith able to alter his code as he wanted?