No, "References Persist" causes Morrowind to keep an object permanently in memory so that scripts/Result Boxes can reference (use) it even when it's not in the same Cell as the calling object/script. Ownership can only be set to a reference, never to an object. You'll see that when you edit (double-click) an object (in the object window): for objects, there's no "Extra Data" section where you could set an ownership. That "Extra Data" section is only available for References.
At the risk of repeating myself (I'd rather explain it yet another time than leave you confused, so if you still don't get it: ask!
I know that it's confusing at the beginning.):
An
object is the prototype of an item; it defines the item's ID, its mesh, and a couple of other things. A
reference is an instance of an pobject in the gameworld. (When you place a piece of Hound Meat in a Cell, you are not placing the object "Hound Meat", you are placing a reference to the object "Hound Meat". (Basically, you tell the game: I want a piece of "Hound Meat" at this place. I have defined what "Hound Meat" is in its object, so look it up there.")