No. A successful case results in lawful permanent residence following an EB-1 or EB-2 determination, subject to visa availability. Citizenship has its own separate requirements and is not what the program provides; the material is explicit that this is not a purchase of citizenship. Any later naturalisation question should be raised with counsel on its own facts.
Write down what you actually need from the status
People want different things from an immigration outcome: the ability to live and work in the country, schooling for children, visa-free travel on a new passport, or a hedge against instability at home. Only some of those follow from permanent residence. Listing them explicitly lets counsel say which the Gold Card can address and which it cannot, before US$15,000 that is never refunded has already been paid on an assumption.
It is worth separating what a household typically wants from what this route provides, item by item, because the mismatch is usually specific rather than general. Permanent residence supports living and working in the country and schooling for children; it does not provide a passport, does not confer nationality on family members, and does not remove the obligations that come with residence. Where the household's main objective turns out to be one of the things it does not provide, the honest conclusion is that this is the wrong route, and reaching that conclusion before a nonrefundable payment is the entire value of asking early.