Spock probably would
have been drugged the same way Kirk was, if the drugging happened the way we saw it (or rather did not see) - without hyposprays or other visible means. That is, anybody beaming down would have received the drug in gaseous form in the fake transporter room...
...And probably continued to receive it throughout his stay in the replica. It didn't seem as if Spock's beam-down actually activated anything or alerted anybody, so the means of drugging would have to be "passive" like that anyway.
Not that I'd think this to be the best way to explain the "exact but completely inoperative" duplicate. More probably, the Gideonites simply obtained the blueprints of this decades-old vessel, along with some photographs, and built some relevant parts of this while blocking access to the unbuilt parts by introducing "inoperative" doors and turbolifts.