No. The Gold Card is not a conventional visa category; under the official framework the gift and processing fee operate within existing immigrant eligibility rules. The applicant must still satisfy the eligibility basis that applies, and the terms should be re-verified before any payment.
Eligibility comes before the gift, not after it
The executive order and program materials describe a mechanism in which a gift to the U.S. government is treated as relevant to eligibility under existing immigrant provisions, subject to the determinations the government makes. That means an applicant is still assessed on the basis the program identifies, and the gift does not by itself create a right to an immigrant visa or permanent residence.
For a veterinarian, the practical questions are which category the program applies, what background and admissibility review will occur, and what documentation of her qualifications and history is expected. Because the program is new and its terms have been published through official channels that may be updated, every statement here should be checked against the current program page before acting. A professional who commits funds on the basis of a summary from a seminar, rather than the official text, has confused a payment with an approval.