Generally speaking, parole is granted to Cuban nationals who cannot be returned to Cuba. In this case, you are describing someone who can be removed to Canada. Parole is granted in the exercise of discretion and is not obtainable as a matter of right. Whether CBP would do so in this case most likely depends on a number of different factors that would need to be evaluated. Keep in mind that employment authorization is not immediately issued but takes a number of months to get, even when an alien is paroled in the public interest.
I recommend that the person consult with an experienced immigration attorney for case specific advice.
While this answer is provided by a Florida Bar Certified Expert in Immigration and Nationality Law, it is for general information purposes only and an attorney/client relationship is neither intended nor created. You should seek out qualified counsel to review your case and provide you with advice specific to your situation. Call +1-561-478-5353 to schedule a consultation with Mr. Devore.
It depends on the CBP officer and can vary depending on the port of entry. If they see him as a Canadian citizen, they may not give him a Cuban parole. If he enters and stays for one year, regardless of how he entered, he will be able to apply for residence under the CAA after that year. But if he doesn't have parole, he won't be able to get a work permit that first year. In my experience, I have seen clients have more luck obtaining a parole when they enter by land at a port of entry on the border and show their Cuban passport/birth certificate.
The information offered is general in nature and not meant to be relied upon as legal advice. No client-attorney relationship is created through this information. Please consult an attorney prior to making legal decisions.