One of my friends is a drag entertainer but also a cis woman, at work she would constantly be told that she was a man, and customers would constantly insist that she was 'actually a man'.
What she experienced was comparable to gender dysphoria, however I wouldn't ever compare cis people having similar experiences with trans identifying people - most trans people experience mental, physical and social dysphoria, whereas cis people who experience dysphoria have it triggered socially.