Almost certainly. While neither his writings, nor those of his son Moroni, explicitly speak of their ordination to the Priesthood, we know that Mormon served as a church leader in his time, struggling to teach what remained of his people and stave off their encroaching descent into apostasy. Such leadership requires proper authority and Priesthood ordination.
See Moroni chapter 8, consisting of an epistle written by Mormon to Moroni, in which he mentions his leadership role in the church and speaks to clarify certain points of doctrine, with an explanation which he received by revelation from the Lord. Latter-Day Saints believe that any person can receive revelation, but only covering themselves or matters which they personally have stewardship over. Therefore, in order to receive revelation regarding doctrinal matters affecting the entire church, he would have needed to be someone with responsibility for the entire church.
As for the original point raised in the question:
Before [the restoration of the Priesthood in modern days], there were several figures of note according to the book of Mormon well after the original 12 apostles' time. Not the least of which was Mormon himself.
Because Mormon existed before the moment where the priesthoods were reestablished though Joesph Smith, I had this question come to mind: Was Mormon himself a priest in the sense that the Aaronic and Melchizedek priests are in the LDS today?
The state of general apostasy that necessitated the restoration of the church and the priesthood was not immediate upon the death of the original apostles, either in the Old World or among the Nephites. It was instead a gradual process, as described in 4 Nephi. Mormon mentions how the church prospered for a long time, but then as contentions and divisions began to arise among the people, the church began to decay along with it. In 4 Nephi verses 24-40, he describes how they went from a state of harmonious unity to societal division and widespread sectarian violence over the course of about forty years, and this was still almost a hundred years before Mormon and Moroni's day, when the apostasy among the Nephite people finally became complete.