No i don't think Tam was a warder, Moiraine clearly says he was second in command of the companions in Illian. He almost certainly had contact to warders in the Aiel war, and there are other elite groups beside warders, for all we know the companions are one of those. But Tam may have had contact to a warder and training by him in Illian. Somewhere it's mentionned that the king of illian has an aes sedai councillor and as second commander of the companions Tam must have been close to the king, what if he trained with the warder of that unknow sedai.