and while I would not recommend drinking the stuff by making a slurry of permethrin dust and water, in a healthy human permethrin is rapidly broken down by protein reactions on the skin (and within our digestive tract), filtered by the liver, and excreted. Medically significant one time doses are quite large in volume - much more than the trace amounts measurable in an egg.
The same is true of almost every mammal (except cats - they lack a needed enzyme).