Yes, if you are eating a meal that you just ordered from the children’s menu, tuck away, otherwise, no. Napkins stay on your lap — if you have to leave the table, they go on the chair, not the table, as no one wants to see the physical evidence of what you’ve wiped off of your face.
The only other expectation to when it is ok to tuck a napkin into your shirt is if you are applying pressure to a wound. Which shouldn’t be done at the table, anyways.
~ Karen Cleveland