No, fake ESA letters do not work. This is because the letter’s authenticity can be easily established, and you may get into trouble otherwise.
For people with disabilities, a fake ESA letter is the ultimate insult. It makes it difficult for those who really need this certification to get around in society.
Moreover, those who fake such letters may be considered frauds - punishable by jail time and fines - due to misleading authorities into believing that someone needs an ESA when that is not true.