Class of languages able to be recognized equal to $\text{P}/\text{poly}$?

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Let us say notationally that an oracle Turing machine satisfies property $(*)$ if all queries it makes to the oracle are of the form$$\text{11}\ldots{1}.$$Question. Is the class of languages that are able to be recognized by a polynomial time, of property $(*)$, oracle machine with any oracle equal to $\text{P}/\text{poly}$?