Bilge. There was no draft between the Civil War and WWI, IIRC, and we did just fine with national identity.
Nobody who cares about winning in combat wants the draft back, it was a freakin' disaster and the Army and Air Force didn't really finish recovering from it until a decade after Vietnam.
Say what you will, but I believe that jet travel, the massification of education, and the diversification of popular media have done more to fragement national identity than anything else.