Here I googled "Working illegally on a K-1 Visa", do as you see fit.
Working on a K-1 Visa: Risk of Working Without an EAD
That being said, if you work illegally while in the United States on your K-1 visa, you would be in direct violation of your K-1 visa status expectations. You then risk your opportunity to adjust your status and will not be able to apply for or receive a green card.
Some people decide to work illegally while they are awaiting clearance to work with a pending K-1 visa. Working illegally is a violation of your visa status—and if you're not in valid visa status, you're not eligible to adjust status and get a green card. Consult an immigration attorney for details.