No. The official framework requires the application and processing fee, vetting, admissibility and an available visa in the resulting EB-1 or EB-2 classification. The gift is a condition of the process, not a substitute for the legal requirements of permanent residence.
Read the gift as one step in a legal process
The official page sets out a sequence in which money is not the first step. An applicant submits an application and a nonrefundable processing fee, undergoes vetting, and is instructed to make the gift only after that stage. Permanent residence then follows through an existing immigrant classification, which means the ordinary grounds of inadmissibility apply, and a visa number must be available under the Visa Bulletin for the applicant's country of chargeability.
A Sainte-Catherine-de-la-Jacques-Cartier applicant should therefore start with the same admissibility review any immigrant would undertake: criminal history, past U.S. immigration compliance, health and security questions. The page does not describe an exemption from those grounds, and nothing in it describes the gift as buying a result.
If the page's terms have changed since this review, the current version governs, and the household should re-verify before submitting anything.