I sincerely doubt that any regulatory body could take enforcement action against a person from putting “Joe Blow, B.A.Sc. mechanical engineering” or the like on their business card or e-mail signature, if indeed that person had proof of the degree in question.
If the person put the words “professional”, “licensed”, “certified”, “registered” etc. in front of “engineer”, they’re in trouble because they’re holding themselves out to have a license that they do not possess, potentially misleading the public.
If the person lists their TITLE as “mechanical engineer”, they MAY be in trouble in some jurisdictions and WILL be in trouble in others, because this implies that their job description includes engineering that, depending on the jurisdiction, may require a license to perform.
As to whether the threat of enforcement against misuse of title is a credible one, that also depends on your jurisdiction. If you have a licensed colleague or client who has a bee in their bonnet about licensure requirements, they may (in fact they may have a DUTY to) complain against you, at which point the threatening letter will come in- and it’ll go to your boss, not just to you. In our jurisdiction, you are generally sent a cease and desist letter rather than being handed a fine automatically.
Common work-arounds for non-licensed engineers include avoiding listing a job title at all, rather choosing to put “Engineering department” etc. on their card. “Project manager”, “technical specialist” etc. are also popular.