I have to admit, this is my least favourite question. I dislike it even more than “Is that your best price?” and “Can you have the job finished before I host my daughter’s wedding in 2 weeks?”
First of all, working under the table is illegal. But if you're considering it at all, this apparently doesn't bother you, so I'll move onto other issues that might. Without any sort of written agreement between you and your contractor (kitchen or otherwise) you have little if any legal recourse if the project goes sideways. Assuming the court will even hear your case without any form of documentation, they’d have to resort to your word against the contractor’s. I can almost guarantee that won’t work well in your favour.
The purchaser in the first design firm I worked for had a poster on her wall that I feel summarizes this situation nicely:
My quote includes a quality product, quality installation and quality service. You want a lower price? What would you have me remove from my quote?