No, this is the very heart of Searle's thought experiment. His point was that you could imagine a rule-based system for language translation and conversation that clearly was not conscious. The argument wasn't about whether or not it was possible to build such a system, but about whether or not such a system must necessarily be conscious.
Searle's claim was that it was clear from his thought experiment that such a system could exist without any understanding, and definitely without consciousness. Others have disagreed with his reasoning and his conclusion.
I must have misunderstood your earlier comment then. I thought you were saying that Searle responded to ”the system does understand” argument by saying “OK, but it’s still not conscious.” Now I think you are saying his response was “no, it doesn’t understand, it merely passes the Turing test; it can’t understand because it’s clearly not conscious.” Which again, seems to beg the question.
No, Searle's main response to the system response was to just dismiss it out of hand (at least in the responses from him that I read). Dennett was probably (for me) the most articulate of the "system responders" and I think Searle considered his POV to be a joke, more or less.
Searle's claim was that it was clear from his thought experiment that such a system could exist without any understanding, and definitely without consciousness. Others have disagreed with his reasoning and his conclusion.