While I doubt the AOs will be communicating with the financial aid office, I’d caution against revealing your parent’s under-the-table job anywhere in your college app. Without knowing how detailed you’re going to be in your essay, or why your parent works under the table, I’d still say it’s too much of a risk.
And while I sympathize with undocumented people or citizens simply trying to make ends meet, I’d personally never pay someone under the table nor have I ever failed to report income I easily could have omitted. At the very least, you may run afoul of your AO’s feelings on the ethics of the matter.