Not while the work is performed in Canada. The Gold Card becomes relevant only if the worker wants to live and work in the United States permanently, and even then it must be compared with TN, L-1 and ordinary EB-1 or EB-2 routes.
Identify the change that would require permission before pricing the card
Hypothetical example: A Portugal Cove-St. Philip's architect who codes at home for a U.S. client and visits for meetings is not working in the United States, and no U.S.
work authorization is required for the Canadian-based work. The question changes if the company wants the architect on site regularly, wants to put the architect on its U.S. payroll, or the architect wants permanent residence.
For on-site temporary work, TN is available to a Canadian citizen in a listed profession such as computer systems analyst with a bachelor's degree, and L-1 may be available if the Canadian corporation and the U.S. company are related. For permanent residence, the ordinary EB-1 and EB-2 categories exist with employer sponsorship or, in some cases, self-petition.
Under the official framework, the gift is treated as evidence for the applicable EB-1 or EB-2 basis, but admissibility, visa availability and any remaining category requirements still apply. Paying for it without first identifying which change actually needs permission is a mistake.