Yes. The person he saw die is unknown for certain.
An exact date of Rubeus' father's death is never given, nor any details of its circumstances. He could have died during one of the vacations, or could have fallen ill, and Rubeus was granted leave to visit him.
Or he could have missed his father's death and witnessed some other death prior to becoming Gamekeeper.
The fact that hes the only wizard known to have succeeded in taming Thestrals, and that Hogwarts has been using Thestrals to pull its carriages for some time before Harry came to the school, its safe to assume Hagrid has been able to see Thestrals for quite some time.
Hagrid told Madame Maxime that he was 13 when his father died. Hagrid was also a charter member of the Order of the Phoenix during the First Wizarding War which saw a lot of deaths. They had been losing when Voldemort tried to kill Harry and had his killing curse rebound on him due to Lily's protectiive magic in Harry.