Short answer: Yes.
Long answer: As demonstrated repeatedly since Warcraft 3, one of the criteria for raising a death knight is that this person has to draw the attention of the Scourge or the Ebon Blade as a noteworthy individual, otherwise the Scourge/Ebon Blade would be wasting their time attempting to raise this person as a Death Knight instead of adding them to the pile of mindless Scourge (or used as cannon fodder/ghouls, for the Ebon Blade). Legion goes out of its way to reinforce this point, as every Death Knight you raise as part of the Order Hall questline is someone who was a person of importance in life, and has been dead for some time now (twice over, in Darion's case). Sally Whitemane, High Inquisitor of the Scarlet Crusade, General Nazgrim of the Horde, King Thoras Trollbane of Stromgarde, and Highlord Darion Mograine of the Ebon Blade are all names worth knowing.
There is no reason to assume that the allied races and pandaren who are made death knights didn't undergo the process of death, revival, and training that the rest of the Ebon Blade did; it's just that (like the regular allied race PCs) you're skipping their initiation process to play one ready to stand battle. So far, Arthas and Bolvar remain unique in that there's no evidence they died before getting their powers as death knights. Every other example we've gotten involves someone who had to die first. What's worth noting is that your death knight, like the rest, was somebody before they died. I'd take current lore into account and odds are good you either died in the Fourth War or during the current war against N'Zoth.
After Shadowlands launches, odds are, like the WotLK death knights, you died in the pre-expansion Scourge invasion event in canon, but the starting quest is ambiguous enough to give you wiggle room as to when you died--you could stretch it from a roleplay perspective and say you had died during the events of Legion, if you want to. The Ebon Blade has certainly been busy raising death knights all across the board, as the nameless NPC troops evidence, and the last two wars have left them no shortage of dead heroes to initiate into the order.
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Going by A Special Surprise, Forsaken death knights are exceptionally unlucky. You break free only to fall back under the Scourge's sway, only this time you're elite cannon fodder rather than regular cannon fodder.