No. The fee starts vetting; it is not a status, and the gift and the underlying immigrant process follow it. Until that process is complete the applicant's existing status, or lack of one, governs what he may do in the United States.
Nothing in the sequence is a permission to relocate
The published order is processing fee, vetting, gift on official instruction, and then the steps of the EB-1 or EB-2 immigrant process, ending in permanent residence after approval, visa availability and the remaining immigrant processing. None of the earlier stages authorizes residence or work. A Paradise applicant who has paid the fee remains, for immigration purposes, exactly what he was the day before: a Canadian citizen who may visit for permitted visitor activities and may not work without a status that allows it.
An intermediary who suggests otherwise is describing something the official page does not. The official FAQ currently says the process should take weeks, but that is an estimate rather than a guaranteed deadline, so a house sale, lease or business relocation should not depend on it. Any interim U.S.
business activity is a separate nonimmigrant question. Re-verify the official page before money or relocation commitments move.