More so than being a felon in the first place? Most places won't let felons get a foot in the door in the first place. Unless not-checking that box is a criminal offense, lying about your qualifications hasn't stopped some of the highest offices in the US being filled, so while it's easy to say "don't check the box", it's just as easy to say (and just as unrealistic, unless you have a time machine), to say "don't be a felon", to somebody that already has the conviction. Which is to say, it isn't really helpful.

More realistically, the (un)likelyhood of a felony conviction going unnoticed on a background check means that whether or not you check the box, if the employer does a background check it will become known, but some places don't run the check and some don't actually care about the results but they're required to run the check.

So a low chances of being fired is better than a zero chance of being hired? If it isn't immediately pertinent to the applicant's ability to do the job, for example if a convicted sex offender were applying for a position as a child caretaker, and the offender has paid their due to society then the employer has no right to ask. Everything but that type of conflict of interest should be treated as personal information. It's the justice system's job to serve justice, not the responsibility of HR.