No, Egyptian is an adjective used to describe something of or from Egypt (a proper noun). Although Egyptian is an adjective, it is still capitalized.
Egyptian is the proper adjective for Egypt.
The word Egyptian is a proper noun as a word for a person of or from the country of Egypt. The word Egyptian is also a proper adjective that describes a noun as of or from the country of Egypt.
The proper adjective for southwest is "southwestern."
The proper adjective is Haitian.
The proper adjective for Portuguese is "Portuguese."
Vietnamese is the proper adjective for Vietnam.
The proper adjective for George is Georgian.
Mayan is itself a proper adjective.
The proper adjective for Siam is Siamese.
The proper adjective for Georgia is Georgian.
Freudian is the proper adjective for Freud.