Is the $631 filing fee that I paid to the federal government for my pardon/criminal record suspension tax deductible?

No, you are not able to claim this on your tax return.

Can you deduct on income tax

As Jeffrey said above, no. Generally, you can only deduct legal fees that you paid:

• while earning of income from a business or property
• to collect salary/wages from an employer
• to collect a retiring allowance or pension benefit
• in certain child support situations
• to fight the CRA

This blog post talks more about what legal fees are deductible: https://turbotax.intuit.ca/tips/are-all-legal-fees-fully-tax-deductible-6542

In the case of legal fees to collect salary/wages, it has to be for money that’s actually owed, not “potential” money such as a possible raise that could come with a promotion. In this Financial Post article, they talk about some prior rulings as to what was and was not deductible: https://business.financialpost.com/legal-post/vern-krishna-cra-rules-make-it-tough-for-employees-to-deduct-professional-fees