No. The official framework describes the gift as one step in a process that also requires vetting, eligibility for the EB-1 or EB-2 classification as determined by the authorities, admissibility, and an available visa number. Ability to pay is necessary to the process but decides none of those.
What the gift does and does not settle
Read the official FAQ for what it actually promises: an application, a fee, vetting, further instructions from USCIS, the gift when instructed, and then the ordinary immigrant-visa or adjustment steps for the classification assigned. Each of those stages has conditions the money cannot satisfy. Vetting looks at the applicant's history. Eligibility for the classification is determined by the authorities on the applicant's facts. Admissibility applies the same grounds — criminal, security, health, prior violations, misrepresentation — that apply to any intending immigrant. Visa availability follows the bulletin. Hypothetical example: an East Hants applicant with a decades-old conviction assumes the gift makes it irrelevant; it does not, and the fee is nonrefundable if the case fails on admissibility. Before paying anything, have the household's immigration history reviewed against the admissibility grounds, because that review is cheap and the processing fee is not returned.
Hypothetical example: an East Hants antique-watch restorer receives an online offer to submit the payment through a private concierge. The first review should identify the official application instruction, the applicant's own eligibility evidence, and the official payment direction for a payment made only when instructed. A consultant's receipt does not prove an official payment or overcome a history issue. The decision is whether to pay a nonrefundable processing charge before obtaining advice on a known admissibility question, not whether a gift can erase that question.