I have had this discussion before with some other shooting enthusiasts and this is what we collectively decided; all in our opinions, of course.
Since the range of the M1/M2 carbine is at the edge of the maximum range that the majority of small arms combat takes place (300-400yds), has FA capacity, the rifle is shorter and lighter than a full size battle rifle, but larger and more powerful than a sub-machine gun, the M2 carbine in fact does fit the description of the "assault rifle" criteria. Camparing the M2 carbine to the German StG44, the cartridges have very similar performances and the rifles have similar ranges, and mag capacity is the same. The StG44 is a bit heavier and bulkier, but much of that has to do with materials the weapons were made of.
I claim not to be an expert, and I did not consult any of my manuals before typing this response, but do think that the M2 does in fact qualify as an assault rifle in a military sense, but a weaker one at that. Perhaps more a long range sub-gun than an assault rifle?
JRB