Nope. Memories shape who you are but don't determine who you are. Digitizing them then shoving them all into a .exe with a series of if/thens designed to make the program act in a reasonable facsimile does not make that program a person.
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This is true, and Elidibus himself probably brings the clearest example, albeit in a bit of a sideways way. (Spoiler-ing the rest because I think the OP might still be in post-Stormblood.)
I've described current Elidibus as 'a self-portrait of a self-portrait', basically one person's gradually distorted view of themselves over millennia of being the core/an extension of Zodiark.
He's a very extreme version, though, that's someone tempered by themselves across twelve thousand years. Yotsuyu would probably have never lived long enough to show that. ...especially because she's naturally a very stubborn person, there's a good chance you cure her tempering and she doesn't even notice.
(SHB AND EW SPOILERS)
If you've done the Bozja questline it's also why the ancient Gunnhildr's Blades felt so threatened when the shrine maiden they chose had the Echo. They made their plan with the assumption she'd be tempered by the transformation.
I know Emet-Selch claimed Zodiark tempered his summoners but the Loporrits said tempering was added to the primal summoning process after the Sundering. Maybe Elidibus ended up how he did because he'd already died in the initial summoning.