No, it wouldn't. The federal government is one of limited, enumerated powers, and none of the enumerated powers is to disarm the populace. The entire BOR is a belt-and-suspenders arrangement, to emphasize the limit of the grant of power to the federal government, in particular aspects.
Separately, I get a laugh out of "only" the militia. The militia is ALL people capable of bearing arms. When the populace is armed, and knows how to use the arms, then the populace comprises a free state.
Now that I think about it, I think you are right. There was a heated discussion about the inclusion of the BOR because many believed it could be construed that rights not included were excluded. Rights are inherent in the individual.