No, the Supreme Court made no decision, because the record didn't say whether or not a short barrel shotgun had a military or "common (as in "for all of us," not as in "many people have them") defense" use. The case was sent back to the court that found the NFA to be unconstitutional, and that ruling (NFA is unconstitutional in light of the second amendment) holds if the weapon being taxed is found to have a military use.
From memory, one of the key phrases in the SCOTUS opinion is "absent evidence, we cannot say." Then it went on to say how the decision below should be reached - if the evidence showed the weapon to have a military use, then the NFA was afoul of the 2nd amendment.
Miller was never even tried, let alone convicted. His indictment was quashed on 2nd amendment grounds.
The National Firearms Act as applied to transporting in interstate commerce a 12-gauge shotgun with a barrel less than 18 inches long, without having registered it and without having in his possession a stamp-affixed written order for it was not unconstitutional as an invasion of the reserved powers of the States and did not violate the Second Amendment of the United States Constitution.
My understanding is that the lower court had declared that short barreled shotguns had a military use and therefore could not be taxed (restricted) under the NFA. The US Supreme Court remanded that District Court decision which had supported the legality of short barreled shotguns. The USSC upheld the NFA.
The notion that such shotguns had no military use was a central (and erroneous) determinant.