I guess it all depends on what exact Constitution you would be referencing.
In Pennsylvania the term "permit-less carry" would be synonymous with "Constitutional Carry" because of the Pennsylvania State Constitution that clearly and simply states:
Right to Bear Arms
The right of the citizens to bear arms in defense of themselves and the State shall not be questioned.
Many States have their own individual Constitutions which reaffirm the God Granted right to keep and bear arms even though politicians have perverted it, undermined it, and/or just flat out ignored it.