Not necessarily.
If a person dresses up as a Military officers, gains access to a base, and gives orders, do those order need to be carried out?
If a person fakes a law degree, becomes a member of the bar, and later becomes a judge, are their decisions and judgements in court valid?
If a person dresses up like a police officer and makes an arrest, is the arrest valid?
If a person fakes citizenship and becomes President, are their signatures valid?
Even your link says that if a person acts to deceive then the third part is not bound.
If a person fakes a medical degree, joins the AMA, gets hired by a hospital, and removes an appendix... should the appendix be re-inserted?
If a Coke addicted Kenyan works as a male prostitute in NY, can he use that experience for College Credits at Columbia University?
These are the vexing questions of our time.