yeah, but without a soul, ICARUS would literaly just be a thing. A simulation of a mind, even less of a mind than HILDA, who at least got this void stuff going on where you seemingly never have a soul. But ICARUS has no relation to the void whatsoever. For ICARUS, the distinction between having a soul and not having a soul is the difference between being a person and a toaster.
Well, the answer to that question might be solved by shoving her into the nearest TV and seeing if a Shadow forms. If it does, she has a soul. If not, well, we tried.
And Kyle is firmly believes that souls are bullshit as no one has shown him proof of it that is concrete. Which is what happened last time. If he does have a soul he will remove it as it is unessessary.
Uh....yeah, the only ways someone can perform soulectomy on themselves is to die, throw themselves into the Void and hope for the best, or a lot of painful experiments which will probably result in him dying first.
Hell, Kyle IS proof they exist; say hi, Merlin.