No they don't. Extraordinarii and Italian Spearmen did not fight the "Roman" way, the manipular system, so they did not get the advantage of the Stamina rules. The stamina rule is a "subterfuge" to try and apply to the rules the extremely diffult way of fighting of the roman army of the period. Triplex Acies and so on. As the army book point out, in the erlier period of the list the italian (or latin) allied of the roman keep their way of fighting and only later they adopt the legion formation in the roman way. Roman and latin allies that forms units of hastati, principes, triarii and rorarii have the benefit of the stamina rules, to try to replicate on the table the way of fighting of a Consular army of the later period of the list, formed by two legiions of romans and two legions of latin. For what I do understand, and that's how we play.