Yes, the possessive form of a proper noun can act as an adjective.
The proper adjective is "American," derived from the proper noun "America."
"Chicago" can be a noun (referring to a city) or an adjective (describing something related to the city).
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.
No, old is not a proper adjective. A proper adjective is an adjective derived from a proper noun, such as Swiss cheese, Bolivian pottery, Chinese silk, etc.
The proper adjective for Georgia is Georgian.
The proper adjective for George is Georgian.
Freudian is the proper adjective for Freud.
Mayan is itself a proper adjective.