I think the motivations and organization of this "1rst North American Expeditionary Force" is rather different from the Special Service Force of the Boer War or the "Mac-Paps" from the Spanish Civil War, so drawing analogies are going to be difficult, if not downright inaccurate.
The primary issue here is these are individuals who are motivated to go by personal reasons, and who are essentially joining as individual foreign mercenaries augmenting a tribal force. Perhaps the most realistic historical analogy might be adventurers going to Ethiopia in the 1930's to fight the Italians (but even that isn't quite right, since there was an "Imperial" government of sorts in charge of Ethiopia at the time).
I suspect the people going over to assist will be horribly disillusioned by the end of their ordeal, as they will not have much in the way of manpower and resources to add to the cause, and I imagine many bureaucratic obstacles will spring up in their path both going over and returning home. If the "Expeditionary Force" could muster battalion sized groups of volunteers (500+) with adequate logistical support (including medical services), then they probably *could* make a noticeable difference, but this also presupposes that the Kurds would be open to what amounts to a foreign military force operating on their territory.
Still, their hearts are in the right place, and for what it is worth I wish them well.