Yes, std::set, std::multiset, std::map, and std::multimap are all sorted using std::less as the default comparison operation. The underlying data-structure used is typically a balanced binary search tree such as a red-black tree. So if you add an element to these data-structures and then iterate over the contained elements, the output will be in sorted order. The complexity of adding N elements to the data-structure will be O(N log N), or the same as sorting a vector of N elements using any common O(log N) complexity sort.
In your specific scenario, since you don’t have key/value pairs, std::set or std::multiset is probably your best bet.