No, it doesn't. You miss the main point: the added mass means more tension for the given diameterl at the same pitch. Since the nickel is in the wrap, as with all strings, the wrap is essentially nothing more than a slinky (the toy) coil around the core adding mass. The same thing with piano strings: pure copper is so soft it doesn't have any real modulus of elasticity either (hence all the bad jokes about folks who are so stingy they stretch a penny into wire). But the core is steel, which bears the tension and the pitch to piano bass strings the same way as any wound string, bass, guitar, etc. The core is still steel, so, respectfully, your point is not on point.
Read both the GHS and the D'Addadario string guides: string construction has nothing to do with tension. T (Tension) = (UW x (2 x L x F)2 ) / 386.4 . UW is unit weight, the mass of the string. Nothing else determines tension. Now, depending on the rest of the variables of string construction, including the stiffness of the core, hex or round, the way the wraps are applied to the core, the type of wrap and how they lay on the core, etc., can affect feel and flexibility, but does not affect tension. But don't take my word for it: this is what
@Jon Moody , bass player and member of this forum, product r&d at GHS strings taught me. He knows more about bass strings than the rest of us put together. I stand by my post. Everybody else: go take a physics course like I did in school, especially the chapter on harmonic motion and what affects frequency, which we hear as pitch.